Ptaszyński Krzysztof
Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland.
Phys Rev E. 2022 Aug;106(2-1):024119. doi: 10.1103/PhysRevE.106.024119.
Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to dynamics and thermodynamics of a transport setup. Specifically, several distinct bounds on these quantities are either analytically derived or numerically conjectured, which are applicable to (1) noninteracting fermionic systems, (2) noninteracting bosonic systems, (3) thermally driven classical Markovian systems, and (4) unicyclic Markovian networks. Finally, it is demonstrated that violation of the obtained inequalities can provide a broad spectrum of information about the physics of the analyzed system; e.g., it can enable one to infer the presence of interactions or unitary dynamics, unravel the topology of the Markovian network, or characterize the nature of thermodynamic forces driving the system. In particular, relevant information about the microscopic dynamics can be gained even at equilibrium when the current variance-a standard measure of current fluctuations-is determined mostly by the thermal noise.
电流涨落是揭示所观测输运过程潜在物理机制的有力工具。本文讨论了与输运体系的动力学和热力学相关的第三和第四电流累积量（偏度和峰度）的一些一般性质。具体而言，这些量的几个不同界限要么通过解析推导得出，要么通过数值推测得到，它们适用于：（1）非相互作用费米子系统；（2）非相互作用玻色子系统；（3）热驱动经典马尔可夫系统；（4）单循环马尔可夫网络。最后，证明违反所得到的不等式能够提供关于被分析系统物理机制的广泛信息；例如，它能使人们推断相互作用或幺正动力学的存在，揭示马尔可夫网络的拓扑结构，或刻画驱动系统的热力学力的性质。特别地，即使在平衡态，当电流方差（电流涨落的标准度量）主要由热噪声决定时，也能获得有关微观动力学的相关信息。
