期刊
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
卷 392, 期 1, 页码 123-135出版社
ELSEVIER
DOI: 10.1016/j.physa.2012.08.019
关键词
Irreversible thermodynamics; Markov process; Cross graining
We investigate the internal consistency of a recently developed mathematical thermodynamic structure across scales, between a continuous stochastic nonlinear dynamical system, i.e., a diffusion process with Langevin and Fokker-Planck equations, and its emergent discrete, inter-attractoral Markov jump process. We analyze how the system's thermodynamic state functions, e.g. free energy F, entropy S. entropy production e(p), free energy dissipation (F) over dot, etc., are related when the continuous system is described with coarse-grained discrete variables. It is shown that the thermodynamics derived from the underlying, detailed continuous dynamics gives rise to exactly the free-energy representation of Gibbs and Helmholtz. That is, the system's thermodynamic structure is the same as if one only takes a middle road and starts with the natural discrete description, with the corresponding transition rates empirically determined. By natural we mean in the thermodynamic limit of a large system, with an inherent separation of time scales between inter- and intra-attractoral dynamics. This result generalizes a fundamental idea from chemistry, and the theory of Kramers, by incorporating thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described by a discrete representation, in terms of exponential rate laws and a stochastic thermodynamics. (C) 2012 Elsevier B.V. All rights reserved.
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