不可逆热力学中Glansdorff-Prigogine稳定性判据的再探讨
Revisiting the Glansdorff-Prigogine criterion for stability within irreversible thermodynamics
摘要：
Glansdorff和Prigogine（1970）提出了熵产生率的分解，今天主要被称为Hatano-Sasa方法。他们的背景是不可逆热力学，虽然忽略了波动，但仍然允许比基于Master或Fokker-Planck方程的处理更广泛。Glansdorff和Prigogine首先提出了过剩熵产生率$δ^2$ EP的概念，并提出$δ^2$ EP为正是非平衡宏观条件稳定性的充分判据。我们发现，非线性扩散，它们的过剩熵产生率本身是当地的自由能，这是接近平衡的功能，管理宏观波动的时间导数。过剩的$δ^2$ EP的积极性，我们国家的一个简单的充分条件，因此是等价的单调性在时间上的功能在放松到稳定的非平衡。也出现了一个关系，最近扩展的克劳修斯热定理接近平衡。$δ^2$ EP的正性直接意味着过剩热量的克劳修斯（不）等式。最后一个相关的问题涉及涨落泛函、非平衡自由能的操作意义，以及它们如何进入不可逆热力学。
英文摘要：
Glansdorff and Prigogine (1970) proposed a decomposition of the entropy production rate, which today is mostly known for Markov processes as the Hatano-Sasa approach. Their context was irreversible thermodynamics which, while ignoring fluctuations, still allows a somewhat broader treatment than the one based on the Master or Fokker-Planck equation. Glansdorff and Prigogine were the first to introduce a notion of excess entropy production rate $δ^2$EP and they suggested as sufficient stability criterion for a nonequilibrium macroscopic condition that $δ^2$EP be positive. We find for nonlinear diffusions that their excess entropy production rate is itself the time-derivative of a local free energy which is the close-to-equilibrium functional governing macroscopic fluctuations. The positivity of the excess $δ^2$EP, for which we state a simple sufficient condition, is therefore equivalent with the monotonicity in time of that functional in the relaxation to steady nonequilibrium. There also appears a relation with recent extensions of the Clausius heat theorem close-to-equilibrium. The positivity of $δ^2$EP immediately implies a Clausius (in)equality for the excess heat. A final and related question concerns the operational meaning of fluctuation functionals, nonequilibrium free energies, and how they make their entrée in irreversible thermodynamics.
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