Investigating Information Geometry in Classical and Quantum Systems through Information Length

Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length [Formula: see text] to quantify information change associated with a time-dependent PDF that depends on time. [Formula: see text] is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of [Formula: see text] in understanding information change and attractor structure in classical and quantum systems.