Information dynamics: Temporal behavior of uncertainty measures

TL;DR

This paper systematically studies uncertainty measures in dynamical processes using information theory, analyzing how Fisher and Shannon information inequalities relate to the temporal evolution of probability densities across different systems.

Contribution

It introduces a framework for analyzing the compatibility of information inequalities with the temporal behavior of probability densities in various dynamical systems.

Findings

Identifies conditions under which Fisher and Shannon inequalities hold over time.

Provides insights into the temporal evolution of uncertainty in deterministic, random, and quantum systems.

Establishes a basis for future analysis of information measures in complex dynamical processes.

Abstract

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on a compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.