论文标题
扩展不可逆热力学中熵的统计基础
The Statistical Foundation of Entropy in Extended Irreversible Thermodynamics
论文作者
论文摘要
在扩展的不可逆热力学（EIT）的理论中，依赖通量的熵函数起着关键作用，并且与通常的不依赖磁通的熵函数具有基本的区别。但是，它的存在是EIT的先决条件，其统计来源从未有理由是合理的。 In this work, by studying the macroscopic limit of an ε-dependent Langevin dynamics, which admits a large deviations (LD) principle, we show that the stationary LD rate functions of probability density p_ε(x; t) and joint probability density p_ε(x; \dot{x}; t) actually turn out to be the desired fluxindependent entropy function in CIT and flux-dependent entropy function分别在EIT中。两个熵函数的差异取决于布朗运动时间的时间分辨率，而后者是由LD Hamilton-Jacobi方程式产生的，可用于构建保守的Lagrangian/Hamiltonian动力学。
In the theory of extended irreversible thermodynamics (EIT), the flux-dependent entropy function plays a key role and has a fundamental distinction from the usual flux-independent entropy function adopted by classical irreversible thermodynamics (CIT). However, its existence, as a prerequisite for EIT, and its statistical origin have never been justified. In this work, by studying the macroscopic limit of an ε-dependent Langevin dynamics, which admits a large deviations (LD) principle, we show that the stationary LD rate functions of probability density p_ε(x; t) and joint probability density p_ε(x; \dot{x}; t) actually turn out to be the desired fluxindependent entropy function in CIT and flux-dependent entropy function in EIT respectively. The difference of the two entropy functions is determined by the time resolution for Brownian motions times a Lagrangian, the latter arises from the LD Hamilton-Jacobi equation and can be used for constructing conserved Lagrangian/Hamiltonian dynamics.
