Spinney Richard E, Ford Ian J
Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 May;85(5 Pt 1):051113. doi: 10.1103/PhysRevE.85.051113. Epub 2012 May 10.
Total entropy production and its three constituent components are described both as fluctuating trajectory-dependent quantities and as averaged contributions in the context of the continuous Markovian dynamics, described by stochastic differential equations with multiplicative noise, of systems with both odd and even coordinates with respect to time reversal, such as dynamics in full phase space. Two of these constituent quantities obey integral fluctuation theorems and are thus rigorously positive in the mean due to Jensen's inequality. The third, however, is not and furthermore cannot be uniquely associated with irreversibility arising from relaxation, nor with the breakage of detailed balance brought about by nonequilibrium constraints. The properties of the various contributions to total entropy production are explored through the consideration of two examples: steady-state heat conduction due to a temperature gradient, and transitions between stationary states of drift diffusion on a ring, both in the context of the full phase space dynamics of a single Brownian particle.
总熵产生及其三个组成部分，既被描述为依赖于波动轨迹的量，也被描述为在连续马尔可夫动力学背景下的平均贡献。这种动力学由具有乘性噪声的随机微分方程描述，适用于具有相对于时间反演奇偶坐标的系统，如全相空间中的动力学。这些组成量中的两个服从积分涨落定理，因此由于詹森不等式，其平均值严格为正。然而，第三个组成量并非如此，而且它既不能唯一地与弛豫产生的不可逆性相关联，也不能与非平衡约束导致的细致平衡的破坏相关联。通过考虑两个例子来探讨对总熵产生的各种贡献的性质：一个是由于温度梯度引起的稳态热传导，另一个是单个布朗粒子在全相空间动力学背景下在环上的漂移扩散的稳态之间的跃迁。
