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Tangde VM, Bhalekar AA. How Flexible Is the Concept of Local Thermodynamic Equilibrium? ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25010145. [PMID: 36673286 PMCID: PMC9858024 DOI: 10.3390/e25010145] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 12/26/2022] [Accepted: 12/31/2022] [Indexed: 06/01/2023]
Abstract
It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x˜k,j} corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions.
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Affiliation(s)
- Vijay M. Tangde
- Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India
| | - Anil A. Bhalekar
- Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India
- 106, Himalaya Prestige, South Ambazari Marg, SBI Colony, Gopal Nagar, Nagpur 440 022, India
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Gujrati PD. A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1584. [PMID: 34945890 PMCID: PMC8700608 DOI: 10.3390/e23121584] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Revised: 11/14/2021] [Accepted: 11/15/2021] [Indexed: 11/17/2022]
Abstract
The review deals with a novel approach (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space SZ involving internal variables as additional state variables. The IEQ macrostates are unique in SZ and have no memory just as EQ macrostates are in the EQ state space SX⊂SZ. The approach provides a clear strategy to identify the internal variables for any model through several examples. The MNEQT deals directly with system-intrinsic quantities, which are very useful as they fully describe irreversibility. Because of this, MNEQT solves a long-standing problem in NEQT of identifying a unique global temperature T of a system, thus fulfilling Planck's dream of a global temperature for any system, even if it is not uniform such as when it is driven between two heat baths; T has the conventional interpretation of satisfying the Clausius statement that the exchange macroheatdeQflows from hot to cold, and other sensible criteria expected of a temperature. The concept of the generalized macroheat dQ=deQ+diQ converts the Clausius inequality dS≥deQ/T0 for a system in a medium at temperature T0 into the Clausius equalitydS≡dQ/T, which also covers macrostates with memory, and follows from the extensivity property. The equality also holds for a NEQ isolated system. The novel approach is extremely useful as it also works when no internal state variables are used to study nonunique macrostates in the EQ state space SX at the expense of explicit time dependence in the entropy that gives rise to memory effects. To show the usefulness of the novel approach, we give several examples such as irreversible Carnot cycle, friction and Brownian motion, the free expansion, etc.
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Affiliation(s)
- Purushottam D. Gujrati
- Department of Physics, The University of Akron, Akron, OH 44325, USA;
- Department of Polymer Science, The University of Akron, Akron, OH 44325, USA
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Bazant MZ. Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis. Faraday Discuss 2017; 199:423-463. [DOI: 10.1039/c7fd00037e] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn–Hilliard and Allen–Cahn equations. The Glansdorff–Prigogine stability criterion is extended for driving chemical work, based on variations of nonequilibrium Gibbs free energy. Linear stability is generally determined by the competition of chemical diffusion and driven autocatalysis. Novel features arise for electrochemical systems, related to controlled total current (galvanostatic operation), concentration-dependent exchange current (Butler–Volmer kinetics), and negative differential reaction resistance (Marcus kinetics). The theory shows how spinodal decomposition can be controlled by solo-autocatalytic charge transfer, with only a single faradaic reaction. Experimental evidence is presented for intercalation and electrodeposition in rechargeable batteries, and further applications are discussed in solid state ionics, electrovariable optics, electrochemical precipitation, and biological pattern formation.
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Affiliation(s)
- Martin Z. Bazant
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
- Department of Mathematics
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Mandal A, Hunt KLC. Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: complete separation and physical interpretation. J Chem Phys 2012; 137:164109. [PMID: 23126697 DOI: 10.1063/1.4750045] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
When a time-dependent perturbation acts on a quantum system that is initially in the nondegenerate ground state ∣0> of an unperturbed Hamiltonian H(0), the wave function acquires excited-state components ∣k> with coefficients c(k)(t) exp(-iE(k)t/ℏ), where E(k) denotes the energy of the unperturbed state ∣k>. It is well known that each coefficient c(k)(t) separates into an adiabatic term a(k)(t) that reflects the adjustment of the ground state to the perturbation--without actual transitions--and a nonadiabatic term b(k)(t) that yields the probability amplitude for a transition to the excited state. In this work, we prove that the energy at any time t also separates completely into adiabatic and nonadiabatic components, after accounting for the secular and normalization terms that appear in the solution of the time-dependent Schrödinger equation via Dirac's method of variation of constants. This result is derived explicitly through third order in the perturbation. We prove that the cross-terms between the adiabatic and nonadiabatic parts of c(k)(t) vanish, when the energy at time t is determined as an expectation value. The adiabatic term in the energy is identical to the total energy obtained from static perturbation theory, for a system exposed to the instantaneous perturbation λH'(t). The nonadiabatic term is a sum over excited states ∣k> of the transition probability multiplied by the transition energy. By evaluating the probabilities of transition to the excited eigenstates ∣k'(t)> of the instantaneous Hamiltonian H(t), we provide a physically transparent explanation of the result for E(t). To lowest order in the perturbation parameter λ, the probability of finding the system in state ∣k'(t)> is given by λ(2) ∣b(k)(t)∣(2). At third order, the transition probability depends on a second-order transition coefficient, derived in this work. We indicate expected differences between the results for transition probabilities obtained from this work and from Fermi's golden rule.
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Affiliation(s)
- Anirban Mandal
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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Trepagnier EH, Jarzynski C, Ritort F, Crooks GE, Bustamante CJ, Liphardt J. Experimental test of Hatano and Sasa's nonequilibrium steady-state equality. Proc Natl Acad Sci U S A 2004; 101:15038-41. [PMID: 15469914 PMCID: PMC524055 DOI: 10.1073/pnas.0406405101] [Citation(s) in RCA: 198] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Most natural processes occur far from equilibrium and cannot be treated within the framework of classical thermodynamics. In 1998, Oono and Paniconi [Oono, Y. & Paniconi, M. (1998) Prog. Theor. Phys. Suppl. 130, 29-44] proposed a general phenomenological framework, steady-state thermodynamics, encompassing nonequilibrium steady states and transitions between such states. In 2001, Hatano and Sasa [Hatano, T. & Sasa, S. (2001) Phys. Rev. Lett. 86, 3463-3466] derived a testable prediction of this theory. Specifically, they were able to show that the exponential average of Y, a quantity similar to a dissipated work, should be equal to zero for arbitrary transitions between nonequilibrium steady states, -ln = 0. We have tested this strong prediction by measuring the dissipation and fluctuations of microspheres optically driven through water. We have found that -ln approximately 0 for three different nonequilibrium systems, supporting Hatano and Sasa's proposed extension of thermodynamics to arbitrary steady states and irreversible transitions.
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Affiliation(s)
- E H Trepagnier
- Biophysics Graduate Group, University of California, Berkeley, CA 94720, USA
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Nieuwenhuizen TM, Allahverdyan AE. Statistical thermodynamics of quantum Brownian motion: construction of perpetuum mobile of the second kind. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:036102. [PMID: 12366179 DOI: 10.1103/physreve.66.036102] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2000] [Revised: 05/02/2002] [Indexed: 05/23/2023]
Abstract
The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a nontrivial role, namely, when the bath temperature T is smaller than the coupling energy. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low T. Various formulations of the second law are found to be invalid at low T. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. In this process the energy put on the particle does not relax monotonically, but oscillates between particle and bath, even in the limit of strong damping. Third, for nonadiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobility of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g., those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale variant Planck's over 2pi /k(B)T is larger than or comparable to other time scales of the system. They show that there is no general consensus between standard thermodynamics and quantum mechanics. The known agreements occur only due to the weak coupling limit, which does not pertain to low temperatures. Experimental setups for testing the effects are discussed.
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Affiliation(s)
- Th M Nieuwenhuizen
- Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, The Netherlands
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Luzzi R, Vasconcellos ÁR, Jou D, Casas-Vázquez J. Thermodynamic variables in the context of a nonequilibrium statistical ensemble approach. J Chem Phys 1997. [DOI: 10.1063/1.474976] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Peric M, Morriss GP. Free energy and entropy production in planar Couette flow far from equilibrium. Mol Phys 1995. [DOI: 10.1080/00268979500100731] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Vlad MO, Ross J. Thermodynamic approach to nonequilibrium chemical fluctuations. J Chem Phys 1994. [DOI: 10.1063/1.467265] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Casas-Vázquez J, Jou D. Nonequilibrium temperature versus local-equilibrium temperature. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:1040-1048. [PMID: 9961311 DOI: 10.1103/physreve.49.1040] [Citation(s) in RCA: 91] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Weider T, Glaser MA, Hanley HJ, Clark NA. Shear-induced melting of two-dimensional solids. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:5622-5628. [PMID: 10004508 DOI: 10.1103/physrevb.47.5622] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Jou D, Casas-Vázquez J. Possible experiment to check the reality of a nonequilibrium temperature. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:8371-8373. [PMID: 9906935 DOI: 10.1103/physreva.45.8371] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Zheng Q, Ross J, Hunt KLC, Hunt PM. Stationary solutions of the master equation for single and multi‐intermediate autocatalytic chemical systems. J Chem Phys 1992. [DOI: 10.1063/1.462446] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hunt PM, Hunt KLC, Ross J. Thermodynamic and stochastic theory for nonequilibrium systems with more than one reactive intermediate: Nonautocatalytic or equilibrating systems. J Chem Phys 1990. [DOI: 10.1063/1.457950] [Citation(s) in RCA: 31] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Hunt KLC, Hunt PM, Ross J. On Liapunov functions for single‐variable reacting systems displaced from equilibrium. J Chem Phys 1989. [DOI: 10.1063/1.456113] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ross J, Hunt KLC, Hunt PM. Thermodynamics far from equilibrium: Reactions with multiple stationary states. J Chem Phys 1988. [DOI: 10.1063/1.454002] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Keizer J. Nonequilibrium chemical potentials and free energies for enzyme-catalyzed reactions. CELL BIOPHYSICS 1987; 11:331-44. [PMID: 2450667 DOI: 10.1007/bf02797128] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Using the statistical theory of nonequilibrium thermodynamics we explore the nature of nonequilibrium corrections to chemical potentials in simple enzyme-catalyzed reactions. The statistical definition of the chemical potential, which pertains to systems that are at stable steady states, is applied to the Michaelis-Menten reaction scheme in a cellular-sized compartment that communicates with outside reservoirs. Calculations based on the kinetic parameters for hexokinase and triose phosphate isomerase show that substantial corrections to the chemical potential of product (the order of 25 mV) are possible if the reaction is sufficiently far from equilibrium. The dependence of the corrections to the chemical potentials on the size of the cellular compartment are explored, and the relevance of the corrections for understanding the thermodynamics of metabolites is discussed.
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Affiliation(s)
- J Keizer
- Institute of Theoretical Dynamics, University of California, Davis 95616
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Keizer J, Chang O. The nonequilibrium electromotive force. I. Measurements in a continuously stirred tank reactor. J Chem Phys 1987. [DOI: 10.1063/1.452911] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Keizer J. The nonequilibrium electromotive force. II. Theory for a continuously stirred tank reactor. J Chem Phys 1987. [DOI: 10.1063/1.452912] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rodríguez RF, García‐Colín LS, del Castillo LF. Fluids with internal degrees of freedom. I. Extended thermodynamics approach. J Chem Phys 1987. [DOI: 10.1063/1.451880] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jou D, Ferrer‐Suquet F, Perez CJ. On the nonequilibrium chemical potential of open pores in a membrane. J Chem Phys 1986. [DOI: 10.1063/1.451674] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mou CY, Luo J, Nicolis G. Stochastic thermodynamics of nonequilibrium steady states in chemical reaction systems. J Chem Phys 1986. [DOI: 10.1063/1.450623] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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