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Kobayashi M, Nakagawa N, Sasa SI. Control of Metastable States by Heat Flux in the Hamiltonian Potts Model. PHYSICAL REVIEW LETTERS 2023; 130:247102. [PMID: 37390420 DOI: 10.1103/physrevlett.130.247102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 05/15/2023] [Indexed: 07/02/2023]
Abstract
The local equilibrium thermodynamics is a basic assumption of macroscopic descriptions of the out of equilibrium dynamics for Hamiltonian systems. We numerically analyze the Hamiltonian Potts model in two dimensions to study the violation of the assumption for phase coexistence in heat conduction. We observe that the temperature of the interface between ordered and disordered states deviates from the equilibrium transition temperature, indicating that metastable states at equilibrium are stabilized by the influence of a heat flux. We also find that the deviation is described by the formula proposed in an extended framework of the thermodynamics.
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Affiliation(s)
- Michikazu Kobayashi
- School of Engeneering Science, Kochi University of Technology, Miyanoguchi 185, Tosayamada, Kami, Kochi 782-8502, Japan
| | - Naoko Nakagawa
- Department of Physics, Ibaraki University, Mito 310-8512, Japan
| | - Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502 Japan
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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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Sasa SI, Nakagawa N, Itami M, Nakayama Y. Stochastic order parameter dynamics for phase coexistence in heat conduction. Phys Rev E 2021; 103:062129. [PMID: 34271670 DOI: 10.1103/physreve.103.062129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 05/29/2021] [Indexed: 06/13/2023]
Abstract
We propose a stochastic order parameter model for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a nonequilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in nonequilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a superheated ordered (supercooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in Nakagawa and Sasa [Liquid-Gas Transitions in Steady Heat Conduction, Phys. Rev. Lett. 119, 260602 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.260602.].
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Affiliation(s)
- Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Naoko Nakagawa
- Department of Physics, Ibaraki University, Mito 310-8512, Japan
| | - Masato Itami
- Department of Physics, Nagoya University, Nagoya 464-8602, Japan
| | - Yohei Nakayama
- Department of Applied Physics, Tohoku University, Sendai 980-8579, Japan
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Nakagawa N, Sasa SI. Liquid-Gas Transitions in Steady Heat Conduction. PHYSICAL REVIEW LETTERS 2017; 119:260602. [PMID: 29328708 DOI: 10.1103/physrevlett.119.260602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Indexed: 06/07/2023]
Abstract
We study liquid-gas transitions of heat conduction systems in contact with two heat baths under constant pressure in the linear response regime. On the basis of local equilibrium thermodynamics, we propose an equality with a global temperature, which determines the volume near the equilibrium liquid-gas transition. We find that the formation of the liquid-gas interface is accompanied by a discontinuous change in the volume when increasing the mean temperature of the baths. A supercooled gas near the interface is observed as a stable steady state.
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Affiliation(s)
- Naoko Nakagawa
- Department of Physics, Ibaraki University, Mito 310-8512, Japan
| | - Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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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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González-Díaz PF. Wormholes and thermodynamics. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1996; 54:1856-1859. [PMID: 10020861 DOI: 10.1103/physrevd.54.1856] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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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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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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Eu BC, Bhattacharya DK. Modified-moment method for the Fokker-Planck equation and some aspects of the thermodynamics of irreversible processes. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:3597-3608. [PMID: 9901663 DOI: 10.1103/physreva.39.3597] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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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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Ramaswamy S, Renn SR. Theory of shear-induced melting of colloidal crystals. PHYSICAL REVIEW LETTERS 1986; 56:945-948. [PMID: 10033327 DOI: 10.1103/physrevlett.56.945] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Keizer J. Heat, work, and the thermodynamic temperature at nonequilibrium steady states. J Chem Phys 1985. [DOI: 10.1063/1.448273] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Keizer J. The coupling of density and internal energy fluctuations by isothermal chemical reactions. J Chem Phys 1984. [DOI: 10.1063/1.447247] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Lebon G, Jou D. A nonclassical thermodynamic description of heat conducting viscous fluids. J Chem Phys 1982. [DOI: 10.1063/1.443873] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Thermodynamics of Nonequilibrium Processes. ACTA ACUST UNITED AC 1979. [DOI: 10.1007/978-3-642-67480-8_24] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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