AI 中文总结
该研究将克拉美-罗不等式推广至非平衡定态，得到含能量涨落、响应与费舍尔信息的普适关系，在平衡态退化为涨落-响应关系，并通过三类模型验证。
AI 中文摘要
平衡定态完全由仅依赖能量和温度的玻尔兹曼分布描述。相比之下，描述大量物理和生物现象的非平衡定态通常复杂得多，其定态分布可依赖诸多动力学参数。非平衡统计力学的核心挑战是识别在这种复杂性下仍适用于非平衡定态的普适关系。本文证明，克拉美-罗不等式的一种形式适用于任意非平衡定态分布，且不依赖动力学参数的显式依赖。该结果的一个主要原创特征是，此不等式在平衡态下会退化为已知的涨落-响应关系。该不等式涉及三个明确定义的量：能量的涨落、平均能量对逆温度的导数给出的响应，以及对逆温度的费舍尔信息。我们用三个代表性模型说明该不等式：简谐势中的活性粒子、动力学校对的简单方案，以及两个热浴间热传导的一维模型。
英文摘要
Equilibrium steady states are fully characterized by the Boltzmann distribution, which depends only on the energy and the temperature. In contrast, nonequilibrium steady states, which describe a wide range of physical and biological phenomena, are generically much more complex, and their stationary distributions can depend on a zoo of kinetic parameters. A central challenge of nonequilibrium statistical mechanics is the identification of universal relations that hold for nonequilibrium steady states despite this complexity. We show here that a form of the Cramer-Rao inequality applies to arbitrary nonequilibrium steady-state distributions and contains no explicit dependence on kinetic parameters. A main original feature in our observation is that this inequality becomes a well-known fluctuation-response relation in equilibrium. The inequality involves three well-defined quantities: the fluctuations of the energy, the response given by the derivative of the average energy with respect to the inverse temperature, and the Fisher information with respect to the inverse temperature. We illustrate this inequality using three representative models: an active particle in a harmonic potential, a simple scheme for kinetic proofreading, and a one-dimensional model for heat conduction between two baths.
Comments8 pages, 3 figures
