Stochastic thermodynamics is an important development in the direction of finding general thermodynamic principles for non-equilibrium systems. We believe stochastic thermodynamics has the potential to benefit from the measure-theoretic framework of stochastic differential equations (SDEs). Toward this, in this work, we show that fluctuation theorem (FT) is a special case of the Girsanov theorem, which is an important result in the theory of SDEs. We report that by employing Girsanov transformation of measures between the forward and the reversed dynamics of a general class of Langevin dynamic systems, we arrive at the integral fluctuation relation. Following the same approach, we derive the FT also for the overdamped case. Our derivation is applicable to both transient and steady state conditions and can also incorporate diffusion coefficients varying as a function of state and time, e.g. in the context of multiplicative noise. We expect that the proposed method will be an easy route towards deriving the FT irrespective of the complexity and non-linearity of the system.

中文翻译：

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涨落定理作为吉尔萨诺夫定理的特例

随机热力学是寻找非平衡系统一般热力学原理方向的重要发展。我们相信随机热力学有可能受益于随机微分方程 (SDE) 的测度理论框架。为此，在这项工作中，我们证明了涨落定理（FT）是吉尔萨诺夫定理的一个特例，它是 SDE 理论中的一个重要结果。我们报告说，通过在一般类朗之万动力系统的正向和反向动力学之间采用吉尔萨诺夫测度变换，我们得到了积分涨落关系。按照相同的方法，我们也得出了过阻尼情况下的 FT。我们的推导适用于瞬态和稳态条件，并且还可以结合随状态和时间而变化的扩散系数，例如在乘性噪声的情况下。我们期望所提出的方法将是推导 FT 的简单途径，无论系统的复杂性和非线性如何。