Karbowski Jan
Institute of Applied Mathematics and Mechanics, Department of Mathematics, Informatics, and Mechanics, <a href="https://ror.org/039bjqg32">University of Warsaw</a>, ul. Banacha 2, 02-097 Warsaw, Poland.
Phys Rev E. 2024 May;109(5-1):054126. doi: 10.1103/PhysRevE.109.054126.
Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well-known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs limitations on the rates of such quantities instead. Here, several general upper bounds on the rates of some f-divergences are derived, valid for any type of stochastic dynamics (both Markovian and non-Markovian), in terms of information-like and/or thermodynamic observables. As special cases, the analytical bounds on the rate of mutual information are obtained. The major role in all those limitations is played by temporal Fisher information, characterizing the speed of global system dynamics, and some of them contain entropy production, suggesting a link with stochastic thermodynamics. Indeed, the derived inequalities can be used for estimation of minimal dissipation and global speed in thermodynamic stochastic systems. Specific applications of these inequalities in physics and neuroscience are given, which include the bounds on the rates of free energy and work in nonequilibrium systems, limits on the speed of information gain in learning synapses, as well as the bounds on the speed of predictive inference and learning rate. Overall, the derived bounds can be applied to any complex network of interacting elements, where predictability and thermodynamics of network dynamics are of prime concern.
统计散度是数据分析、信息论和统计物理学中的重要工具，并且在其界值方面存在着众所周知的不等式。然而，在许多涉及时间演化的情况下，人们反而需要对这类量的变化率加以限制。在此，依据类信息和/或热力学可观测量，推导出了一些f -散度变化率的若干通用上界，这些上界对任何类型的随机动力学（包括马尔可夫和非马尔可夫动力学）均有效。作为特殊情况，得到了互信息变化率的解析界值。在所有这些限制中，时间费希尔信息起着主要作用，它表征了全局系统动力学的速度，其中一些还包含熵产生，这暗示了与随机热力学的联系。实际上，所推导的不等式可用于估计热力学随机系统中的最小耗散和全局速度。给出了这些不等式在物理学和神经科学中的具体应用，包括非平衡系统中自由能和功变化率的界值、学习突触中信息获取速度的限制，以及预测推理速度和学习率的界值。总体而言，所推导的界值可应用于任何相互作用元素的复杂网络，其中网络动力学的可预测性和热力学是首要关注的问题。
