论文标题
波动定理是Girsanov定理的特殊情况
Fluctuation Theorem as a special case of Girsanov Theorem
论文作者
论文摘要
随机热力学是在寻找非平衡系统一般热力学原理方向上的重要发展。我们认为随机热力学有可能受益于随机微分方程的量度理论框架。在这项工作中，我们表明波动定理（FT）是Girsanov定理的特殊情况，这是随机微分方程理论的重要结果。我们报告说，通过利用girsanov的转换，在通用类动态系统的远期和反向动力学之间的措施之间，我们达成了整体波动关系。遵循相同的方法，我们也为过度阻尼的情况得出了FT。我们的推导适用于瞬态和稳态条件，还可以合并扩散系数随状态和时间的函数而变化。我们预计，所提出的方法将是一个简单的途径，无论系统的复杂性和非线性如何，都可以轻松地得出FT。
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. Towards 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 stochastic differential equations. 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. 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.
