信息熵与随机Nambu非平衡热力学中的耗散势
Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics
浏览论文内容
中文总结 AI 辅助
该研究揭示随机Nambu非平衡热力学中耗散势作为稳态准势而非香农熵，并推导了稳态分布、Massieu解释及涨落协方差。
中文摘要 AI 辅助
我们研究了随机Nambu非平衡热力学（NNET）中耗散势 $S_{\mathrm{NB}}$ 与信息熵之间的关系。从纯扩散、梯度流系统以及具有哈密顿旋转流的系统出发，我们推导了包含Nambu流的Fokker-Planck方程的稳态分布。我们证明，当Nambu流保持耗散势不变，且扩散矩阵与输运张量之间满足爱因斯坦型关系时，稳态分布由 $S_{\mathrm{NB}}$ 决定的指数权重所支配。因此，局部自信息与耗散势直接相关，表明 $S_{\mathrm{NB}}$ 不应被等同于香农熵本身，而是作为控制非平衡稳态分布的稳态准势。利用在开放气体-活塞系统（与热浴和外部压力储库耦合）中建立的热力学熵与耗散势之间的区别，我们进一步阐明了 $S_{\mathrm{NB}}$ 的Massieu解释，引入了Nambu正则分布，并在鞍点近似下推导了涨落的协方差。这些结果通过将NNET耗散势识别为非平衡稳态背后的稳态准势，为其提供了统计解释。
英文摘要
We investigate the relationship between the dissipation potential $S_{\mathrm{NB}}$ and information entropy in stochastic Nambu nonequilibrium thermodynamics (NNET). Starting from pure diffusion, gradient-flow systems, and systems with Hamiltonian rotational currents, we derive the stationary distribution of the Fokker--Planck equation including a Nambu flow. We show that, when the Nambu flow preserves the dissipation potential and an Einstein-type relation holds between the diffusion matrix and the transport tensor, the stationary distribution is governed by an exponential weight determined by $S_{\mathrm{NB}}$. Consequently, the local self-information is directly related to the dissipation potential, demonstrating that $S_{\mathrm{NB}}$ should not be identified with the Shannon entropy itself but instead serves as the stationary quasipotential governing the nonequilibrium steady-state distribution. Using the distinction between the thermodynamic entropy and the dissipation potential established for an open gas--piston system coupled to a thermal bath and an external-pressure reservoir, we further clarify the Massieu interpretation of $S_{\mathrm{NB}}$, introduce a Nambu canonical distribution, and derive the covariance of fluctuations within the saddle-point approximation. These results provide a statistical interpretation of the NNET dissipation potential by identifying it as the stationary quasipotential underlying nonequilibrium steady states.
