Dechant Andreas, Sasa Shin-Ichi
Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan;
Department of Physics 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Proc Natl Acad Sci U S A. 2020 Mar 24;117(12):6430-6436. doi: 10.1073/pnas.1918386117. Epub 2020 Mar 9.
We present an approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that the magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and the unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady-state particle transport, the differential mobility is bounded by the diffusivity. For a "virtual" perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady-state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality.
我们提出了一种以涨落-响应不等式（FRI）形式围绕任意非平衡态的响应方法。我们研究了一个可观测量对基础随机动力学微扰的响应。我们发现，响应的大小由未受微扰系统中可观测量的涨落以及描述受微扰和未受微扰系统的概率密度之间的库尔贝克-莱布勒散度从上方界定。这建立了线性响应与信息论概念之间的联系。我们表明，在许多物理情形中，相对熵可以用物理可观测量来表示。作为这个FRI的直接结果，我们表明对于稳态粒子输运，微分迁移率由扩散率界定。对于与局部平均速度成比例的“虚拟”微扰，我们恢复了稳态输运过程的热力学不确定性关系（TUR）。最后，我们使用FRI推导出不确定性关系到任意动力学的推广，这涉及可观测量的高阶累积量。我们提供了一个明确的例子，其中TUR被违反但其推广以等式形式得到满足。
