论文标题
稳定状态的偏度和峰度的界限
Bounds on skewness and kurtosis of steady state currents
论文作者
论文摘要
当前波动是揭示观察到的运输过程的基本物理的强大工具。这项工作讨论了与运输设置的动力学和热力学有关的第三和第四累积（偏度和峰度）的一些一般特性。具体而言，这些数量上的几个不同的界限是分析得出的或数值猜想的，这些界限适用于：1）非互动的费米子系统，2）非互动的波索克尼克系统，3）3）热驱动的古典马尔可夫系统，4）单流环的马尔可夫网络。最后，证明违反所获得的不等式可以提供有关被分析系统物理学的广泛信息，例如，使人们能够推断出相互作用或单位动力学的存在，揭示马克维亚网络的拓扑，或表征驱动系统的热力学性质的性质。特别是，有关微观动力学的相关信息即使在当前方差（一种标准的电流波动量度）时，也可以在平衡下获得，主要是由热噪声确定的。
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, 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., 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.
