Crisanti A, Puglisi A, Villamaina D
CNR-ISC and Dipartimento di Fisica, Università Sapienza - p.le A. Moro 2, Roma 00185, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061127. doi: 10.1103/PhysRevE.85.061127. Epub 2012 Jun 26.
We discuss the relevance of information contained in cross correlations among different degrees of freedom, which is crucial in nonequilibrium systems. In particular we consider a stochastic system where two degrees of freedom X{1} and X{2}-in contact with two different thermostats-are coupled together. The production of entropy and the violation of equilibrium fluctuation-dissipation theorem (FDT) are both related to the cross correlation between X{1} and X{2}. Information about such cross correlation may be lost when single-variable reduced models for X_{1} are considered. Two different procedures are typically applied: (a) one totally ignores the coupling with X{2}; and (b) one models the effect of X{2} as an average memory effect, obtaining a generalized Langevin equation. In case (a) discrepancies between the system and the model appear both in entropy production and linear response; the latter can be exploited to define effective temperatures, but those are meaningful only when time scales are well separated. In case (b) linear response of the model well reproduces that of the system; however the loss of information is reflected in a loss of entropy production. When only linear forces are present, such a reduction is dramatic and makes the average entropy production vanish, posing problems in interpreting FDT violations.
我们讨论了不同自由度之间互相关中所包含信息的相关性，这在非平衡系统中至关重要。特别地，我们考虑一个随机系统，其中与两个不同恒温器接触的两个自由度X₁和X₂相互耦合。熵的产生以及平衡涨落 - 耗散定理（FDT）的违背都与X₁和X₂之间的互相关有关。当考虑X₁的单变量简化模型时，关于这种互相关的信息可能会丢失。通常应用两种不同的方法：（a）一种方法完全忽略与X₂的耦合；（b）另一种方法将X₂的影响建模为平均记忆效应，从而得到一个广义朗之万方程。在情况（a）中，系统与模型之间在熵产生和线性响应方面都会出现差异；后者可用于定义有效温度，但只有在时间尺度充分分离时这些有效温度才有意义。在情况（b）中，模型的线性响应能很好地再现系统的线性响应；然而，信息的丢失反映在熵产生的损失上。当仅存在线性力时，这种简化非常显著，会使平均熵产生消失，这在解释FDT违背问题时会带来困难。
