论文标题
非线性系统的随机热力学和波动定理
Stochastic thermodynamics and fluctuation theorems for non-linear systems
论文作者
论文摘要
我们通过放宽马尔可维亚动力学必须是线性的两个假设来扩展随机热力学，并且平衡分布必须是玻尔兹曼分布。我们表明，如果我们要求在放宽这些假设时执行第二定律，那么它就无法根据香农熵进行配制。但是，如果我们根据广义熵对第二定律进行重新制定，则可以挽救热力学一致性。我们的第一个结果是将非线性主方程的精确形式与精确相关的广义熵相关的方程式，从而导致热力学一致性。然后，我们建立在此结果的基础上，以扩大热力学数量的通常的轨迹级定义，即使两个假设放松，这些定义也是合适的。最后，我们使用这些轨迹级别的定义来得出骗子的延伸版本波动定理和jarzynski平等，当两个假设放松时适用。
We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when those assumptions are relaxed, then it cannot be formulated in terms of Shannon entropy. However, thermodynamic consistency is salvaged if we reformulate the second law in terms of generalized entropy; our first result is an equation relating the precise form of the non-linear master equation to the precise associated generalized entropy which results in thermodynamic consistency. We then build on this result to extend the usual trajectory-level definitions of thermodynamic quantities that are appropriate even when the two assumptions are relaxed. We end by using these trajectory-level definitions to derive extended versions of the Crooks fluctuation theorem and Jarzynski equality which apply when the two assumptions are relaxed.
