1
|
Ourabah K. Superstatistics from a dynamical perspective: Entropy and relaxation. Phys Rev E 2024; 109:014127. [PMID: 38366540 DOI: 10.1103/physreve.109.014127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2023] [Accepted: 01/02/2024] [Indexed: 02/18/2024]
Abstract
Distributions that deviate from equilibrium predictions are commonly observed across a broad spectrum of systems, ranging from laboratory experiments to astronomical phenomena. These distributions are generally regarded as a manifestation of a quasiequilibrium state and can very often be represented as a superposition of statistics, i.e., superstatistics. The underlying idea in this methodology is that the nonequilibrium system consists of a collection of smaller subsystems that remain infinitely close to equilibrium. This procedure has been effectively implemented in a kinetic setting, but thus far, only in the collisionless regime, limiting its scope of application. In this paper, we address the effect of collisions on the relaxation process and time evolution of superstatistical systems. After confronting the superstatistical distributions with experimental and simulation data, relevant to our analysis, we first study the effect of superstatistics on entropy. We explicitly show that, in the absence of long-range interactions, the extensivity of entropy is preserved, albeit influenced by the specific class of temperature fluctuations. Then, we examine how collisions drive the system towards a global equilibrium state, characterized by a maximum entropy, by employing the relaxation time approximation. This allows us to define a dynamical version of superstatistics, characterized by a singular time-varying parameter q(t), which undergoes a continuous evolution towards equilibrium. We show how this approach enables the determination of the evolution of the underlying temperature distribution under the influence of collisions, which act as stochastic forces, gradually narrowing the temperature distribution over time.
Collapse
Affiliation(s)
- Kamel Ourabah
- Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boite Postale 32, El Alia, Algiers 16111, Algeria
| |
Collapse
|
2
|
Lima HS, Tsallis C, Nobre FD. First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model. ENTROPY (BASEL, SWITZERLAND) 2023; 26:25. [PMID: 38248151 DOI: 10.3390/e26010025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Revised: 12/17/2023] [Accepted: 12/22/2023] [Indexed: 01/23/2024]
Abstract
The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size L is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, Th and Tl (Th>Tl), respectively. These particles at the extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators (i=2,⋯,L-1) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier's law for the heat flux is verified numerically, with the thermal conductivity becoming independent of the lattice size in the limit L→∞, scaling with the temperature, as κ(T)∼T-2.25, where T=(Th+Tl)/2. Moreover, the thermal conductance, σ(L,T)≡κ(T)/L, is well-fitted by a function, which is typical of nonextensive statistical mechanics, according to σ(L,T)=Aexpq(-Bxη), where A and B are constants, x=L0.475T, q=2.28±0.04, and η=2.88±0.04.
Collapse
Affiliation(s)
- Henrique Santos Lima
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil
- National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil
| | - Constantino Tsallis
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil
- National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
- Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080 Vienna, Austria
| | - Fernando Dantas Nobre
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil
- National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil
| |
Collapse
|
3
|
Livadiotis G, McComas DJ. Entropy defect in thermodynamics. Sci Rep 2023; 13:9033. [PMID: 37270648 DOI: 10.1038/s41598-023-36080-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2023] [Accepted: 05/29/2023] [Indexed: 06/05/2023] Open
Abstract
This paper describes the physical foundations of the newly discovered "entropy defect" as a basic concept of thermodynamics. The entropy defect quantifies the change in entropy caused by the order induced in a system through the additional correlations among its constituents when two or more subsystems are assembled. This defect is closely analogous to the mass defect that arises when nuclear particle systems are assembled. The entropy defect determines how the entropy of the system compares to its constituent's entropies and stands on three fundamental properties: each constituent's entropy must be (i) separable, (ii) symmetric, and (iii) bounded. We show that these properties provide a solid foundation for the entropy defect and for generalizing thermodynamics to describe systems residing out of the classical thermal equilibrium, both in stationary and nonstationary states. In stationary states, the consequent thermodynamics generalizes the classical framework, which was based on the Boltzmann-Gibbs entropy and Maxwell-Boltzmann canonical distribution of particle velocities, into the respective entropy and canonical distribution associated with kappa distributions. In nonstationary states, the entropy defect similarly acts as a negative feedback, or reduction of the increase of entropy, preventing its unbounded growth toward infinity.
Collapse
Affiliation(s)
- George Livadiotis
- Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08540, USA.
| | - David J McComas
- Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08540, USA
| |
Collapse
|
4
|
Thursch LJ, Lima TA, O'Neill N, Ferreira FF, Schweitzer-Stenner R, Alvarez NJ. Influence of central sidechain on self-assembly of glycine-x-glycine peptides. SOFT MATTER 2023; 19:394-409. [PMID: 36454226 DOI: 10.1039/d2sm01082h] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Low molecular weight gelators (LMWGs) are the subject of intense research for a range of biomedical and engineering applications. Peptides are a special class of LMWG, which offer infinite sequence possibilities and, therefore, engineered properties. This work examines the propensity of the GxG peptide family, where x denotes a guest residue, to self-assemble into fibril networks via changes in pH and ethanol concentration. These triggers for gelation are motivated by recent work on GHG and GAG, which unexpectedly self-assemble into centimeter long fibril networks with unique rheological properties. The propensity of GxG peptides to self-assemble, and the physical and chemical properties of the self-assembled structures are characterized by microscopy, spectroscopy, rheology, and X-ray diffraction. Interestingly, we show that the number, length, size, and morphology of the crystalline self-assembled aggregates depend significantly on the x-residue chemistry and the solution conditions, i.e. pH, temperature, peptide concentration, etc. The different x-residues allow us to probe the importance of different peptide interactions, e.g. π-π stacking, hydrogen bonding, and hydrophobicity, on the formation of fibrils. We conclude that fibril formation requires π-π stacking interactions in pure water, while hydrogen bonding can form fibrils in the presence of ethanol-water solutions. These results validate and support theoretical arguments on the propensity for self-assembly and leads to a better understanding of the relationship between peptide chemistry and fibril self-assembly. Overall, GxG peptides constitute a unique family of peptides, whose characterization will aid in advancing our understanding of self-assembly driving forces for fibril formation in peptide systems.
Collapse
Affiliation(s)
- Lavenia J Thursch
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, PA 19104, USA.
| | - Thamires A Lima
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, PA 19104, USA.
| | - Nichole O'Neill
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, PA 19104, USA.
- Department of Chemistry, Drexel University, Philadelphia, PA 19104, USA.
| | - Fabio F Ferreira
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, São Paulo, Brazil
| | | | - Nicolas J Alvarez
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, PA 19104, USA.
| |
Collapse
|
5
|
Dos Santos MAF, Nobre FD, Curado EMF. Entropic form emergent from superstatistics. Phys Rev E 2023; 107:014132. [PMID: 36797946 DOI: 10.1103/physreve.107.014132] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 12/23/2022] [Indexed: 06/18/2023]
Abstract
The Beck-Cohen superstatistics became an important theory in the scenario of complex systems because it generates distributions representing regions of a nonequilibrium system, characterized by different temperatures T≡β^{-1}, leading to a probability distribution f(β). In superstatistics, some classes have been most frequently considered for f(β), like χ^{2}, χ^{2} inverse, and log-normal ones. Herein we investigate the superstatistics resulting from a χ_{η}^{2} distribution through a modification of the usual χ^{2} by introducing a real index η (0<η≤1). In this way, one covers two common and relevant distributions as particular cases, proportional to the q-exponential (e_{q}^{-βx}=[1-(1-q)βx]^{1/1-q}) and the stretched exponential (e^{-(βx)^{η}}). Furthermore, an associated generalized entropic form is found. Since these two particular-case distributions have been frequently found in the literature, we expect that the present results should be applicable to a wide range of classes of complex systems.
Collapse
Affiliation(s)
- Maike A F Dos Santos
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil
- Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
| | - Fernando D Nobre
- Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
- National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
| | - Evaldo M F Curado
- Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
- National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
| |
Collapse
|
6
|
Qiu H, Xiao D, Wu J, Wu S, Zhong C, Li X, Peng X, Yuan Y, Cai Q, Chang J, Hu T, Hu Z, Zhu Y. Initial measurement of ion nonextensive parameter with geodesic acoustic mode theory. Sci Rep 2022; 12:3412. [PMID: 35233047 PMCID: PMC8888714 DOI: 10.1038/s41598-022-07295-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 02/16/2022] [Indexed: 11/09/2022] Open
Abstract
The consideration of nonextensivity effects is crucial to the accurate diagnosis of plasma parameters; common plasma nonextensive parameters include electron nonextensive parameter and ion nonextensive parameter, and the former can be measured, while the ion nonextensive parameter cannot be measured yet. Here we show the measurement of ion nonextensive parameter of plasma based on the theory of nonextensive geodesic acoustic modes. We assume that the plasma to be measured can be described by nonextensive statistical mechanics, and on this basis, the nonextensive geodesic acoustic mode theory is established. Utilizing this theory, we have measured the ion nonextensive parameter [Formula: see text] which cannot be diagnosed even by a nonextensive single electric probe. Our research points out that the proposed measurement method of ion nonextensive parameter may play a role in plasma diagnosis and will help us to grasp the nonextensivity of plasma more precisely. We hope the proposed method of ion nonextensive parameter diagnosis based on the nonextensive geodesic acoustic mode theory can be the starting point of more complex ion nonextensive parameter diagnosis methods. In addition, the measurement of ion nonextensive parameter is closely related to the study of various plasma waves, instabilities, turbulence and abnormal transport, and a defined and quantitative test of nonextensive geodesic acoustic mode theory will bound up deeply with such developments.
Collapse
Affiliation(s)
- Huibin Qiu
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China. .,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China.
| | - Donghua Xiao
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Junjie Wu
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Shengfa Wu
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Chengjie Zhong
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Xiaobin Li
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Xingkun Peng
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Youlong Yuan
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Qilong Cai
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Jinming Chang
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Tianyi Hu
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Zuozhi Hu
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| | - Yuqing Zhu
- Jiangxi Province Key Laboratory of Fusion and Information Control, Department of Physics, Nanchang University, Nanchang, 330031, China.,NCU-ASIPP Magnetic Confinement Fusion Joint Lab, Institute of Fusion Energy and Plasma Application, Nanchang University, Nanchang, 330031, China
| |
Collapse
|
7
|
Ourabah K. Fingerprints of nonequilibrium stationary distributions in dispersion relations. Sci Rep 2021; 11:12103. [PMID: 34103627 PMCID: PMC8187350 DOI: 10.1038/s41598-021-91455-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Accepted: 05/26/2021] [Indexed: 11/08/2022] Open
Abstract
Distributions different from those predicted by equilibrium statistical mechanics are commonplace in a number of physical situations, such as plasmas and self-gravitating systems. The best strategy for probing these distributions and unavailing their origins consists in combining theoretical knowledge with experiments, involving both direct and indirect measurements, as those associated with dispersion relations. This paper addresses, in a quite general context, the signature of nonequilibrium distributions in dispersion relations. We consider the very general scenario of distributions corresponding to a superposition of equilibrium distributions, that are well-suited for systems exhibiting only local equilibrium, and discuss the general context of systems obeying the combination of the Schrödinger and Poisson equations, while allowing the Planck's constant to smoothly go to zero, yielding the classical kinetic regime. Examples of media where this approach is applicable are plasmas, gravitational systems, and optical molasses. We analyse in more depth the case of classical dispersion relations for a pair plasma. We also discuss a possible experimental setup, based on spectroscopic methods, to directly observe these classes of distributions.
Collapse
Affiliation(s)
- Kamel Ourabah
- Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boite Postale 32, El Alia, Algiers, 16111, Algeria.
| |
Collapse
|
8
|
Lin S, Chen P, Guan L, Shao Y, Hao Y, Li Q, Li B, Weitz DA, Feng X. Universal Statistical Laws for the Velocities of Collective Migrating Cells. ACTA ACUST UNITED AC 2020; 4:e2000065. [DOI: 10.1002/adbi.202000065] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Revised: 06/09/2020] [Indexed: 02/06/2023]
Affiliation(s)
- Shao‐Zhen Lin
- Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| | - Peng‐Cheng Chen
- Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| | - Liu‐Yuan Guan
- Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| | - Yue Shao
- Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| | - Yu‐Kun Hao
- Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| | - Qunyang Li
- AML Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| | - Bo Li
- Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| | - David A. Weitz
- School of Engineering and Applied Sciences Harvard University Cambridge MA 02138 USA
| | - Xi‐Qiao Feng
- Institute of Biomechanics and Medical Engineering Department of Engineering Mechanics Tsinghua University Beijing 100084 China
| |
Collapse
|
9
|
Qiu H, Zhou Z, Peng X, Zhang X, Zhu Y, Gao Y, Xiao D, Bao H, Xu T, Zhang J, Huang T, Zhou J, Ming Z, Xiang P, Yang H, Wang X, Wu D, Ncst Team. Initial measurement of electron nonextensive parameter with electric probe. Phys Rev E 2020; 101:043206. [PMID: 32422841 DOI: 10.1103/physreve.101.043206] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 03/16/2020] [Indexed: 11/07/2022]
Abstract
Theoretical analysis and a large number of experiments have proved that plasma components do not satisfy Boltzmann-Gibbs statistics and can be well described by nonextensive statistical mechanics, while new plasma parameters, electron nonextensive parameters, which are introduced to describe the nonextensive properties of plasma, cannot be diagnosed yet. Here we show measurement of electron nonextensive parameters of plasma with a nonextensive single electric probe. Our results show that nonextensive electric probe may play a role in plasma diagnosis, measuring nonextensivity of plasma and improving diagnostic accuracy of other plasma parameters. We expect the proposed nonextensive single electric probe can be starting point of more complex nonextensive electric probe. In addition, nonextensive electric probe is an important means to study various plasma waves and instability, turbulence, and anomalous transport, and a definite and quantitative test of the theory of nonextensive geodetic acoustic models will be relevant to such development.
Collapse
Affiliation(s)
- Huibin Qiu
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Zhenyu Zhou
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Xingkun Peng
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Xianyang Zhang
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Yuqing Zhu
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Yue Gao
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Donghua Xiao
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Haifeng Bao
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Tianling Xu
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Jia Zhang
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Tianhui Huang
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Jinmao Zhou
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Zhiyi Ming
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Pengfei Xiang
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Hai Yang
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Xiaofeng Wang
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Dongyang Wu
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| | - Ncst Team
- Department of Physics, Nanchang University, JiangXi, Nanchang 330031, China and Jiangxi Province Key Laboratory of Fusion and Information Control, Nanchang University, Jiangxi, Nanchang 330031, China
| |
Collapse
|
10
|
Tsallis C. Beyond Boltzmann-Gibbs-Shannon in Physics and Elsewhere. ENTROPY 2019; 21:e21070696. [PMID: 33267410 PMCID: PMC7515208 DOI: 10.3390/e21070696] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2019] [Accepted: 06/28/2019] [Indexed: 01/15/2023]
Abstract
The pillars of contemporary theoretical physics are classical mechanics, Maxwell electromagnetism, relativity, quantum mechanics, and Boltzmann–Gibbs (BG) statistical mechanics –including its connection with thermodynamics. The BG theory describes amazingly well the thermal equilibrium of a plethora of so-called simple systems. However, BG statistical mechanics and its basic additive entropy SBG started, in recent decades, to exhibit failures or inadequacies in an increasing number of complex systems. The emergence of such intriguing features became apparent in quantum systems as well, such as black holes and other area-law-like scenarios for the von Neumann entropy. In a different arena, the efficiency of the Shannon entropy—as the BG functional is currently called in engineering and communication theory—started to be perceived as not necessarily optimal in the processing of images (e.g., medical ones) and time series (e.g., economic ones). Such is the case in the presence of generic long-range space correlations, long memory, sub-exponential sensitivity to the initial conditions (hence vanishing largest Lyapunov exponents), and similar features. Finally, we witnessed, during the last two decades, an explosion of asymptotically scale-free complex networks. This wide range of important systems eventually gave support, since 1988, to the generalization of the BG theory. Nonadditive entropies generalizing the BG one and their consequences have been introduced and intensively studied worldwide. The present review focuses on these concepts and their predictions, verifications, and applications in physics and elsewhere. Some selected examples (in quantum information, high- and low-energy physics, low-dimensional nonlinear dynamical systems, earthquakes, turbulence, long-range interacting systems, and scale-free networks) illustrate successful applications. The grounding thermodynamical framework is briefly described as well.
Collapse
Affiliation(s)
- Constantino Tsallis
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems–Rua Dr. Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil;
- Santa Fe Institute–1399 Hyde Park Road, Santa Fe, NM 87501, USA
- Complexity Science Hub Vienna–Josefstädter Strasse 39, 1080 Vienna, Austria
| |
Collapse
|
11
|
Plastino AR, Wedemann RS, Curado EMF, Nobre FD, Tsallis C. Nonlinear drag forces and the thermostatistics of overdamped motion. Phys Rev E 2018; 98:012129. [PMID: 30110810 DOI: 10.1103/physreve.98.012129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Indexed: 06/08/2023]
Abstract
Diverse processes in statistical physics are usually analyzed on the assumption that the drag force acting on a test particle moving in a resisting medium is linear on the velocity of the particle. However, nonlinear drag forces do appear in relevant situations that are currently the focus of experimental and theoretical work. Motivated by these developments, we explore the consequences of nonlinear drag forces for the thermostatistics of systems of interacting particles performing overdamped motion. We derive a family of nonlinear Fokker-Planck equations for these systems, taking into account the effects of nonlinear drag forces. We investigate the main properties of these evolution equations, including an H-theorem, and obtain exact solutions of the stretched q-exponential form.
Collapse
Affiliation(s)
- A R Plastino
- CeBio y Secretaría de Investigación, Universidad Nacional del Noroeste de la Província de Buenos Aires, UNNOBA-Conicet, Roque Saenz Peña 456, Junin, Argentina
| | - R S Wedemann
- Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-900 Rio de Janeiro, RJ, Rio de Janeiro, Brazil
| | - E M F Curado
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil
| | - F D Nobre
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil
| | - C Tsallis
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
- Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria
| |
Collapse
|
12
|
Dai S, Quan B, Liang X, Lv J, Yang Z, Ji G, Du Y. Excellent microwave response derived from the construction of dielectric-loss 1D nanostructure. NANOTECHNOLOGY 2018; 29:195603. [PMID: 29473546 DOI: 10.1088/1361-6528/aab1c2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Increasing efforts have recently been devoted to the artificial design and function of nanostructures for their application prospects in catalysis, drug delivery, energy storage, and microwave absorption. With the advantages of natural abundance, low cost, and environment friendliness, a one-dimensional (1D) MnO2 nanowire (MW) is the representative dielectric-loss absorber for its special morphology and crystalline structure. However, its low reflection loss (RL) value due to its thin thickness limits its wide development and application in the microwave absorption field. In this work, artificially designed MnO2@AIR@C (MCs), namely, 1D hollow carbon nanotubes filled with nano-MnO2, were designed and synthesized. It is found that the RL value of the MC is almost lower than -10 dB. Furthermore, the RL value was able to achieve -18.9 dB with an effective bandwidth (-10 dB) of 5.84 GHz at 2.25 mm. Simultaneously, the dielectric and interfacial polarization became stronger while the impedance matching was much better than in the single MWs. Hence, the rational design and fabrication of micro-architecture are essential and MC has great potential to be an outstanding microwave absorber.
Collapse
Affiliation(s)
- Sisi Dai
- College of Material Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China
| | | | | | | | | | | | | |
Collapse
|
13
|
A Generalized Relative ( α, β)-Entropy: Geometric Properties and Applications to Robust Statistical Inference. ENTROPY 2018; 20:e20050347. [PMID: 33265437 PMCID: PMC7512866 DOI: 10.3390/e20050347] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 03/30/2018] [Revised: 04/22/2018] [Accepted: 05/01/2018] [Indexed: 11/17/2022]
Abstract
Entropy and relative entropy measures play a crucial role in mathematical information theory. The relative entropies are also widely used in statistics under the name of divergence measures which link these two fields of science through the minimum divergence principle. Divergence measures are popular among statisticians as many of the corresponding minimum divergence methods lead to robust inference in the presence of outliers in the observed data; examples include the ϕ -divergence, the density power divergence, the logarithmic density power divergence and the recently developed family of logarithmic super divergence (LSD). In this paper, we will present an alternative information theoretic formulation of the LSD measures as a two-parameter generalization of the relative α -entropy, which we refer to as the general ( α , β ) -entropy. We explore its relation with various other entropies and divergences, which also generates a two-parameter extension of Renyi entropy measure as a by-product. This paper is primarily focused on the geometric properties of the relative ( α , β ) -entropy or the LSD measures; we prove their continuity and convexity in both the arguments along with an extended Pythagorean relation under a power-transformation of the domain space. We also derive a set of sufficient conditions under which the forward and the reverse projections of the relative ( α , β ) -entropy exist and are unique. Finally, we briefly discuss the potential applications of the relative ( α , β ) -entropy or the LSD measures in statistical inference, in particular, for robust parameter estimation and hypothesis testing. Our results on the reverse projection of the relative ( α , β ) -entropy establish, for the first time, the existence and uniqueness of the minimum LSD estimators. Numerical illustrations are also provided for the problem of estimating the binomial parameter.
Collapse
|
14
|
|
15
|
Ourabah K, Tribeche M. Quantum entanglement and temperature fluctuations. Phys Rev E 2017; 95:042111. [PMID: 28505779 DOI: 10.1103/physreve.95.042111] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Indexed: 11/07/2022]
Abstract
In this paper, we consider entanglement in a system out of equilibrium, adopting the viewpoint given by the formalism of superstatistics. Such an approach yields a good effective description for a system in a slowly fluctuating environment within a weak interaction between the system and the environment. For this purpose, we introduce an alternative version of the formalism within a quantum mechanical picture and use it to study entanglement in the Heisenberg XY model, subject to temperature fluctuations. We consider both isotropic and anisotropic cases and explore the effect of different temperature fluctuations (χ^{2}, log-normal, and F distributions). Our results suggest that particular fluctuations may enhance entanglement and prevent it from vanishing at higher temperatures than those predicted for the same system at thermal equilibrium.
Collapse
Affiliation(s)
- Kamel Ourabah
- Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boîte Postale 32, El Alia, Algiers 16111, Algeria
| | - Mouloud Tribeche
- Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boîte Postale 32, El Alia, Algiers 16111, Algeria.,Algerian Academy of Sciences and Technologies, Algiers, Algeria
| |
Collapse
|
16
|
Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview. ENTROPY 2017. [DOI: 10.3390/e19010039] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
17
|
Mohammadzadeh H, Adli F, Nouri S. Perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. Phys Rev E 2017; 94:062118. [PMID: 28085371 DOI: 10.1103/physreve.94.062118] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2016] [Indexed: 11/07/2022]
Abstract
We investigate perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. We show that the intrinsic statistical interaction of nonextensive Bose (Fermi) gas is attractive (repulsive) similar to the extensive case but the value of thermodynamic curvature is changed by a nonextensive parameter. In contrary to the extensive ideal classical gas, the nonextensive one may be divided to two different regimes. According to the deviation parameter of the system to the nonextensive case, one can find a special value of fugacity, z^{*}, where the sign of thermodynamic curvature is changed. Therefore, we argue that the nonextensive parameter induces an attractive (repulsive) statistical interaction for z<z^{*} (z>z^{*}) for an ideal classical gas. Also, according to the singular point of thermodynamic curvature, we consider the condensation of nonextensive Boson gas.
Collapse
Affiliation(s)
- Hosein Mohammadzadeh
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| | - Fereshteh Adli
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| | - Sahereh Nouri
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| |
Collapse
|
18
|
Stock C, Rodriguez EE, Lee N, Green MA, Demmel F, Ewings RA, Fouquet P, Laver M, Niedermayer C, Su Y, Nemkovski K, Rodriguez-Rivera JA, Cheong SW. Solitary Magnons in the S=5/2 Antiferromagnet CaFe_{2}O_{4}. PHYSICAL REVIEW LETTERS 2016; 117:017201. [PMID: 27419585 DOI: 10.1103/physrevlett.117.017201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Indexed: 06/06/2023]
Abstract
CaFe_{2}O_{4} is a S=5/2 anisotropic antiferromagnet based upon zig-zag chains having two competing magnetic structures, denoted as the A (↑↑↓↓) and B (↑↓↑↓) phases, which differ by the c-axis stacking of ferromagnetic stripes. We apply neutron scattering to demonstrate that the competing A and B phase order parameters result in magnetic antiphase boundaries along c which freeze on the time scale of ∼1 ns at the onset of magnetic order at 200 K. Using high resolution neutron spectroscopy, we find quantized spin wave levels and measure 9 such excitations localized in regions ∼1-2 c-axis lattice constants in size. We discuss these in the context of solitary magnons predicted to exist in anisotropic systems. The magnetic anisotropy affords both competing A+B orders as well as localization of spin excitations in a classical magnet.
Collapse
Affiliation(s)
- C Stock
- School of Physics and Astronomy and Centre for Science at Extreme Conditions, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - E E Rodriguez
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
| | - N Lee
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
| | - M A Green
- School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
| | - F Demmel
- ISIS Facility, Rutherford Appleton Labs, Chilton, Didcot OX11 0QX, United Kingdom
| | - R A Ewings
- ISIS Facility, Rutherford Appleton Labs, Chilton, Didcot OX11 0QX, United Kingdom
| | - P Fouquet
- Institute Laue-Langevin, 6 rue Jules Horowitz, Boite Postale 156, 38042 Grenoble Cedex 9, France
| | - M Laver
- School of Metallurgy and Materials, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Ch Niedermayer
- Laboratory for Neutron Scattering, Paul Scherrer Institut, CH-5232 Villigen, Switzerland
| | - Y Su
- Jülich Centre for Neuton Science JCNS, Forschungszentrum Jülich GmbH, Outstation at MLZ, Lichtenbergstraße 1, D-85747 Garching, Germany
| | - K Nemkovski
- Jülich Centre for Neuton Science JCNS, Forschungszentrum Jülich GmbH, Outstation at MLZ, Lichtenbergstraße 1, D-85747 Garching, Germany
| | - J A Rodriguez-Rivera
- NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, USA
- Department of Materials Science, University of Maryland, College Park, Maryland 20742, USA
| | - S-W Cheong
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
| |
Collapse
|
19
|
Why the dipolar response in dielectrics and spin-glasses is unavoidably universal. Sci Rep 2016; 6:29021. [PMID: 27366866 PMCID: PMC4929973 DOI: 10.1038/srep29021] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2016] [Accepted: 06/14/2016] [Indexed: 11/16/2022] Open
Abstract
Materials response to electric or magnetic fields is often dominated by the dynamics of dipoles in the system. This is for instance the case of polar dielectrics and many transition metal compounds. An essential and not yet well understood fact is that, despite their structural diversity, dielectric solids exhibit a striking universality of frequency and time responses, sharing many aspects with the behaviour of spin-glasses. In this article I propose a stochastic approach to dipole dynamics within which the “universal frequency response” derives naturally with Debye’s relaxation mechanism as a special case. This formulation reveals constraints to the form of the relaxation functions, which are essential for a consistent representation of the dynamical slowing-down at the spin-glass transition. Relaxation functions with algebraic-, and exponential-tails, as well as damped oscillations, are shown to have a unified representation in which the stable limit of the distribution of waiting-times between dipole flips determines the present type of dynamics.
Collapse
|
20
|
Brito S, da Silva LR, Tsallis C. Role of dimensionality in complex networks. Sci Rep 2016; 6:27992. [PMID: 27320047 PMCID: PMC4913272 DOI: 10.1038/srep27992] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2016] [Accepted: 05/25/2016] [Indexed: 11/21/2022] Open
Abstract
Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form , where the q-exponential form optimizes the nonadditive entropy Sq (which, for q → 1, recovers the Boltzmann-Gibbs entropy). We introduce and study here d-dimensional geographically-located networks which grow with preferential attachment involving Euclidean distances through . Revealing the connection with q-statistics, we numerically verify (for d = 1, 2, 3 and 4) that the q-exponential degree distributions exhibit, for both q and k, universal dependences on the ratio αA/d. Moreover, the q = 1 limit is rapidly achieved by increasing αA/d to infinity.
Collapse
Affiliation(s)
- Samuraí Brito
- Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica e Experimental, Natal-RN, 59078-900, Brazil
| | - L R da Silva
- Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica e Experimental, Natal-RN, 59078-900, Brazil.,National Institute of Science and Technology of Complex Systems, Brazil
| | - Constantino Tsallis
- National Institute of Science and Technology of Complex Systems, Brazil.,Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil, and Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501, USA
| |
Collapse
|
21
|
Bagchi D, Tsallis C. Sensitivity to initial conditions of a d-dimensional long-range-interacting quartic Fermi-Pasta-Ulam model: Universal scaling. Phys Rev E 2016; 93:062213. [PMID: 27415261 DOI: 10.1103/physreve.93.062213] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2015] [Indexed: 06/06/2023]
Abstract
We introduce a generalized d-dimensional Fermi-Pasta-Ulam model in the presence of long-range interactions, and perform a first-principle study of its chaos for d=1,2,3 through large-scale numerical simulations. The nonlinear interaction is assumed to decay algebraically as d_{ij}^{-α} (α≥0), {d_{ij}} being the distances between N oscillator sites. Starting from random initial conditions we compute the maximal Lyapunov exponent λ_{max} as a function of N. Our N≫1 results strongly indicate that λ_{max} remains constant and positive for α/d>1 (implying strong chaos, mixing, and ergodicity), and that it vanishes like N^{-κ} for 0≤α/d<1 (thus approaching weak chaos and opening the possibility of breakdown of ergodicity). The suitably rescaled exponent κ exhibits universal scaling, namely that (d+2)κ depends only on α/d and, when α/d increases from zero to unity, it monotonically decreases from unity to zero, remaining so for all α/d>1. The value α/d=1 can therefore be seen as a critical point separating the ergodic regime from the anomalous one, κ playing a role analogous to that of an order parameter. This scaling law is consistent with Boltzmann-Gibbs statistics for α/d>1, and possibly with q statistics for 0≤α/d<1.
Collapse
Affiliation(s)
- Debarshee Bagchi
- Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
| | - Constantino Tsallis
- Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology of Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
| |
Collapse
|
22
|
Brown P, Smith GN, Hernández EP, James C, Eastoe J, Nunes WC, Settens CM, Hatton TA, Baker PJ. Magnetic surfactants as molecular based-magnets with spin glass-like properties. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:176002. [PMID: 27028571 DOI: 10.1088/0953-8984/28/17/176002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper reports the use of muon spin relaxation spectroscopy to study how the aggregation behavior of magnetic surfactants containing lanthanide counterions may be exploited to create spin glass-like materials. Surfactants provide a unique approach to building in randomness, frustration and competing interactions into magnetic materials without requiring a lattice of ordered magnetic species or intervening ligands and elements. We demonstrate that this magnetic behavior may also be manipulated via formation of micelles rather than simple dilution, as well as via design of surfactant molecular architecture. This somewhat unexpected result indicates the potential of using novel magnetic surfactants for the generation and tuning of molecular magnets.
Collapse
Affiliation(s)
- Paul Brown
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | | | | | | | | | | | | | | | |
Collapse
|
23
|
|
24
|
Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems. ENTROPY 2015. [DOI: 10.3390/e17052853] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
25
|
Budini AA. Extended q-Gaussian and q-exponential distributions from gamma random variables. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052113. [PMID: 26066125 DOI: 10.1103/physreve.91.052113] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2015] [Indexed: 06/04/2023]
Abstract
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q-Gaussian and q-exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q-Gaussian and modified q-exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.
Collapse
Affiliation(s)
- Adrián A Budini
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro Atómico Bariloche, Avenida E. Bustillo Km 9.5, (8400) Bariloche, Argentina and Universidad Tecnológica Nacional (UTN-FRBA), Fanny Newbery 111, (8400) Bariloche, Argentina
| |
Collapse
|
26
|
Nobre FD, Curado EMF, Souza AMC, Andrade RFS. Consistent thermodynamic framework for interacting particles by neglecting thermal noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022135. [PMID: 25768486 DOI: 10.1103/physreve.91.022135] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2014] [Indexed: 06/04/2023]
Abstract
An effective temperature θ, conjugated to a generalized entropy s(q), was introduced recently for a system of interacting particles. Since θ presents values much higher than those of typical room temperatures T≪θ, the thermal noise can be neglected (T/θ≃0) in these systems. Moreover, the consistency of this definition, as well as of a form analogous to the first law of thermodynamics, du=θds(q)+δW, were verified lately by means of a Carnot cycle, whose efficiency was shown to present the usual form, η=1-(θ(2)/θ(1)). Herein we explore further the heat contribution δQ=θds(q) by proposing a way for a heat exchange between two such systems, as well as its associated thermal equilibrium. As a consequence, the zeroth principle is also established. Moreover, we consolidate the first-law proposal by following the usual procedure for obtaining different potentials, i.e., applying Legendre transformations for distinct pairs of independent variables. From these potentials we derive the equation of state, Maxwell relations, and define response functions. All results presented are shown to be consistent with those of standard thermodynamics for T>0.
Collapse
Affiliation(s)
- Fernando D Nobre
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
- National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud, 150 22290-180 Rio de Janeiro-RJ, Brazil
| | - Evaldo M F Curado
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
- National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud, 150 22290-180 Rio de Janeiro-RJ, Brazil
| | - Andre M C Souza
- Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristóvão-SE, Brazil
- National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud, 150 22290-180 Rio de Janeiro-RJ, Brazil
| | - Roberto F S Andrade
- Instituto de Física, Universidade Federal da Bahia, 40210-340 Salvador-BA, Brazil
- National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud, 150 22290-180 Rio de Janeiro-RJ, Brazil
| |
Collapse
|
27
|
Bento EP, Viswanathan GM, da Luz MGE, Silva R. Third law of thermodynamics as a key test of generalized entropies. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022105. [PMID: 25768456 DOI: 10.1103/physreve.91.022105] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2014] [Indexed: 06/04/2023]
Abstract
The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy S and energy U of an arbitrary N-level classical system. Mathematically, the method relies on exact calculation of β=dS/dU in terms of the microstate probabilities p(i). To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy S(κ), which is additive, and the Tsallis entropy S(q), which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for -1<κ<+1, thereby shedding light on why κ is conventionally restricted to this interval. Surprisingly, however, the Tsallis entropy violates the third law for q<1. Finally, we give a concrete example of the power of our proposed method by applying it to a paradigmatic system: the one-dimensional ferromagnetic Ising model with nearest-neighbor interactions.
Collapse
Affiliation(s)
- E P Bento
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal RN, Brazil
| | - G M Viswanathan
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal RN, Brazil
- National Institute of Science and Technology of Complex Systems, Universidade Federal do Rio Grande do Norte, 59078-970 Natal RN, Brazil
| | - M G E da Luz
- Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba PR, Brazil
| | - R Silva
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal RN, Brazil
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, 59610-210 Mossoró RN, Brazil
| |
Collapse
|
28
|
Ehlers G, Stewart J, Deen P, Andersen K. Neutronxyz– polarization analysis at a time-of-flight instrument. EPJ WEB OF CONFERENCES 2015. [DOI: 10.1051/epjconf/20158303004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
29
|
Ourabah K, Tribeche M. Planck radiation law and Einstein coefficients reexamined in Kaniadakis κ statistics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062130. [PMID: 25019747 DOI: 10.1103/physreve.89.062130] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2013] [Indexed: 06/03/2023]
Abstract
Blackbody radiation is reconsidered using the counterpart of the Bose-Einstein distribution in the κ statistics arising from the Kaniadakis entropy. The generalized Planck radiation law is presented and compared to the usual law, to which it reduces in the limiting case κ→0. Effective Einstein's coefficients of emission and absorption are defined in terms of the Kaniadakis parameter κ. It is shown that the Kaniadakis statistics keeps unchanged the first Einstein coefficient A while the second coefficient B admits a generalized form within the present theoretical framework.
Collapse
Affiliation(s)
- Kamel Ourabah
- Plasma Physics Group, Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boîte Postale 32, El Alia, Algiers 16111, Algeria
| | - Mouloud Tribeche
- Plasma Physics Group, Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boîte Postale 32, El Alia, Algiers 16111, Algeria
| |
Collapse
|
30
|
Ribeiro MS, Nobre FD, Tsallis C. Probability distributions and associated nonlinear Fokker-Planck equation for the two-index entropic form S(q,δ). PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052135. [PMID: 25353767 DOI: 10.1103/physreve.89.052135] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2014] [Indexed: 06/04/2023]
Abstract
The probability distributions and associated Fokker-Planck equation of the recently postulated entropic form, S(q,δ), are investigated. This entropy was proposed as an unification of the well-known S(q) of nonextensive-statistical mechanics and S(δ), which appeared lately as a possibly appropriate candidate for the black-hole entropy. The connection between S(q,δ) and a nonlinear Fokker-Planck equation, such as to satisfy an H-theorem, is explored. The stationary-state probability distribution follows a transcendental equation, which is solved numerically for typical values of q and δ. The same transcendental equation is obtained through the maximum-entropy principle, showing that the two procedures are equivalent.
Collapse
Affiliation(s)
- Mauricio S Ribeiro
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil
| | - Fernando D Nobre
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil
| | - Constantino Tsallis
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
| |
Collapse
|
31
|
Tsallis C, Arenas ZG. Nonextensive statistical mechanics and high energy physics. EPJ WEB OF CONFERENCES 2014. [DOI: 10.1051/epjconf/20147100132] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
32
|
Abstract
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions for situations in which a "joiner particle" k pays some form of price to enter a community of size , where costs are subject to economies of scale. Maximizing the Boltzmann-Gibbs-Shannon entropy subject to this energy-like constraint predicts a distribution having a power-law tail; it reduces to the Boltzmann distribution in the absence of economies of scale. We show that the predicted function gives excellent fits to 13 different distribution functions, ranging from friendship links in social networks, to protein-protein interactions, to the severity of terrorist attacks. This approach may give useful insights into when to expect power-law distributions in the natural and social sciences.
Collapse
|
33
|
Nobre FD, Souza AMC, Curado EMF. Effective-temperature concept: a physical application for nonextensive statistical mechanics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061113. [PMID: 23367899 DOI: 10.1103/physreve.86.061113] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2012] [Indexed: 06/01/2023]
Abstract
The H-theorem [(df/dt) ≤ 0] for a free-energy functional, f = u-θs (with u and s representing, respectively, the internal energy and a generalized entropy of a given physical system), has been proven previously by making use of a nonlinear Fokker-Planck equation. Herein we focus on a nonlinear Fokker-Planck equation derived by means of a coarse-graining procedure on the equations of motion of a system of interacting vortices, under overdamped motion, in the absence of thermal noise (T = 0). In this case, we show that the parameter θ is directly related to the density as well as to the interactions among vortices. Generalized quantities such as entropy, internal energy, free energy, and heat capacity are analyzed for varying θ: important relations and physical behavior analogous to those of standard thermodynamics are found, showing that θ plays the role of an effective temperature. Estimates of θ in typical physical situations of different type-II superconductors are presented; in addition to this, possible experimental procedures for varying θ are proposed.
Collapse
Affiliation(s)
- Fernando D Nobre
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.
| | | | | |
Collapse
|
34
|
Beckmann PA, Schneider E. Methyl group rotation,1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation. J Chem Phys 2012; 136:054508. [DOI: 10.1063/1.3677183] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
35
|
da Silva AJ, Lima RF, Moret MA. Nonextensivity and self-affinity in the mammalian neuromuscular junction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041925. [PMID: 22181193 DOI: 10.1103/physreve.84.041925] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2011] [Revised: 07/05/2011] [Indexed: 05/31/2023]
Abstract
We study time series and the spontaneous miniature end-plate potentials (MEPPs) of mammals recorded at neuromuscular junctions using two different approaches: generalized thermostatistics and detrended fluctuation analysis (DFA). Classical concepts establish that the magnitude of these potentials is characterized by Gaussian statistics and that their intervals are randomly displayed. First we show that MEPP distributions adequately satisfy the q-Gaussian distributions that maximize the Tsallis entropy, indicating their nonextensive and nonequilibrium behavior. We then examine the intervals between the miniature potentials via DFA, where the profile of the intervals between events configures a deviation from the expected random behavior. Some possible physiological substrates for these findings are discussed.
Collapse
Affiliation(s)
- A J da Silva
- Departamento de Fisiologia e Biofísica, Instituto de Ciências Biológicas, Universidade Federal de Minas Gerais, CEP 31270-910 Belo Horizonte, Minas Gerais, Brazil.
| | | | | |
Collapse
|
36
|
The Nonadditive Entropy Sq and Its Applications in Physics and Elsewhere: Some Remarks. ENTROPY 2011. [DOI: 10.3390/e13101765] [Citation(s) in RCA: 126] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
37
|
Nobre FD, Rego-Monteiro MA, Tsallis C. Nonlinear relativistic and quantum equations with a common type of solution. PHYSICAL REVIEW LETTERS 2011; 106:140601. [PMID: 21561176 DOI: 10.1103/physrevlett.106.140601] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2010] [Indexed: 05/30/2023]
Abstract
Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common, solitonlike, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of q.
Collapse
Affiliation(s)
- F D Nobre
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ Brazil.
| | | | | |
Collapse
|
38
|
dos Santos BC, Tsallis C. Time evolution towards q-Gaussian stationary states through unified Itô-Stratonovich stochastic equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061119. [PMID: 21230656 DOI: 10.1103/physreve.82.061119] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2010] [Indexed: 05/30/2023]
Abstract
We consider a class of single-particle one-dimensional stochastic equations which include external field, additive, and multiplicative noises. We use a parameter θ ∊ [0,1] which enables the unification of the traditional Itô and Stratonovich approaches, now recovered, respectively, as the θ=0 and θ=1/2 particular cases to derive the associated Fokker-Planck equation (FPE). These FPE is a linear one, and its stationary state is given by a q-Gaussian distribution with q=(τ+2M(2-θ))/(τ+2M(1-θ)<3), where τ ≥ 0 characterizes the strength of the confining external field and M ≥ 0 is the (normalized) amplitude of the multiplicative noise. We also calculate the standard kurtosis κ(₁) and the q-generalized kurtosis κ(q) (i.e., the standard kurtosis but using the escort distribution instead of the direct one). Through these two quantities we numerically follow the time evolution of the distributions. Finally, we exhibit how these quantities can be used as convenient calibrations for determining the index q from numerical data obtained through experiments, observations, or numerical computations.
Collapse
Affiliation(s)
- B Coutinho dos Santos
- Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil.
| | | |
Collapse
|
39
|
Tsallis C, Tirnakli U. Nonadditive entropy and nonextensive statistical mechanics – Some central concepts and recent applications. ACTA ACUST UNITED AC 2010. [DOI: 10.1088/1742-6596/201/1/012001] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|