Abstract Entropy fluctuations with time occur in finite-sized time-evolving dissipative systems. There is a need to comprehend the role of these fluctuations on the fluctuations-averaged entropy generation rate, over a large enough observation time interval. In this non-equilibrium thermodynamic investigation, the Fluctuation Theorem (FT) and Principle of Least Action are re-visited to articulate their implications for dissipative systems. The Principle of Maximum Entropy Production (MaxEP: the entropy generation rate of a dissipative system is maximized by paths of least action) is conceptually identified as the Principle of Least Action for dissipative systems. A Thermodynamic Fusion Theorem that merges the FT and the MaxEP is introduced for addressing the role of fluctuations in entropy production. It identifies “entropy fluctuations” as the “least-action path” for maximizing the time-averaged entropy production in a dissipative system. The validity of this introduced theorem is demonstrated for the case of entropy fluctuations in Rayleigh–Taylor flow instability.

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波动定理与最小作用量原理的热力学合并：瑞利-泰勒不稳定性案例

摘要 随时间的熵涨落发生在有限大小的时间演化耗散系统中。在足够大的观察时间间隔内，需要理解这些波动对波动平均熵产生率的作用。在这项非平衡热力学研究中，我们重新审视了波动定理 (FT) 和最小作用量原理，以阐明它们对耗散系统的影响。最大熵产生原理（MaxEP：耗散系统的熵生成率通过最小作用路径最大化）在概念上被定义为耗散系统的最小作用原理。引入了融合 FT 和 MaxEP 的热力学融合定理，以解决熵产生中波动的作用。它将“熵涨落”识别为在耗散系统中最大化时间平均熵产生的“最少作用路径”。这个引入的定理的有效性在瑞利-泰勒流动不稳定性的熵涨落的情况下得到了证明。