We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

中文翻译：

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不可逆马尔可夫链中力和流的规范结构和正交性


我们讨论了一种规范结构，它为不可逆有限状态马尔可夫链（连续时间）、Onsager 理论和宏观涨落理论（MFT）提供了动态大偏差的统一描述。对于马尔可夫链，该理论涉及概率流与其共轭力之间的非线性关系。在这个框架内，我们展示了如何将力分成广义上彼此正交的两个分量。这种分裂允许将路径速率函数分解为三项，这三项在耗散和收敛到平衡方面具有物理解释。类似的分解适用于级别 2 和级别 2.5 的速率函数。这些结果阐明了熵产生和涨落定理的界限是如何从潜在的动力学规则中产生的。我们讨论了马尔可夫链的这些结果如何与 MFT 中的类似结构相关，MFT 描述了此类微观模型的流体动力学极限。