On the kinetics of the approach to equilibrium

Prigonine, I.; Résibois, Pierre

doi:10.1016/0031-8914(61)90008-8

Cited by 268 publications

(50 citation statements)

References 9 publications

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“…from the Liouville-von Neumann equation for the density matrix, using the standard generalized master equation approach of nonequilibrium statistical mechanics, [45][46][47][48][49] and by subsequently making reasonable assumptions regarding the factorization properties of the nonequilibrium probability distribution of microscopic states over the degrees of freedom of the different subsystems.…”

Section: Introductionmentioning

confidence: 99%

Theory of entropy production in quantum many-body systems

Solano-Carrillo¹,

Millis²

2016

Phys. Rev. B

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We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second and third laws of thermodynamics. For weakly-coupled subsystems of an isolated system, an expression for the long time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.

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Section: Introductionmentioning

confidence: 99%

Theory of entropy production in quantum many-body systems

Solano-Carrillo¹,

Millis²

2016

Phys. Rev. B

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“…The influence of a solvent or another complex environment on a chemical motion has routinely been modeled using the Langevin equation or its generalization [1,2,3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Phase-space geometry of the generalized Langevin equation

Bartsch

2009

The Journal of Chemical Physics

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The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of the system will be constructed, the generalized Langevin equation will be formally rewritten as a pair of coupled ordinary differential equations, and the fundamental geometric structures in phase space will be described. It will be shown that the phase space itself and its geometric structure depend critically on the preparation of the system: A system that is assumed to have been in existence for ever has a larger phase space with a simpler structure than a system that is prepared at a finite time. These differences persist even in the long-time limit, where one might expect the details of preparation to become irrelevant.

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“…1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 In recent work, 16,17,18,19,20 it was suggested that in many instances, the environment is not stationary, and as such a nonstationary version of the GLE would be desirable. In principle, it is easy to write a nonstationary GLE aṡ…”

Section: Introductionmentioning

confidence: 99%

An idealized model for nonequilibrium dynamics in molecular systems

Vogt

Hernandez

2005

The Journal of Chemical Physics

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The irreversible generalized Langevin equation (iGLE) contains a nonstationary friction kernel that in certain limits reduces to the GLE with space-dependent friction. For more general forms of the friction kernel, the iGLE was previously shown to be the projection of a mechanical system with a time-dependent Hamiltonian. [R. Hernandez, J. Chem. Phys. 110, 7701 (1999)] In the present work, the corresponding open Hamiltonian system is further explored. Numerical simulations of this mechanical system illustrate that the time dependence of the observed total energy and the correlations of the solvent force are in precise agreement with the projected iGLE.

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On the kinetics of the approach to equilibrium

Cited by 268 publications

References 9 publications

Theory of entropy production in quantum many-body systems

Theory of entropy production in quantum many-body systems

Phase-space geometry of the generalized Langevin equation

An idealized model for nonequilibrium dynamics in molecular systems

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