Entropic dynamics yields reciprocal relations

TL;DR

This paper demonstrates that entropic dynamics, grounded in information geometry, naturally leads to reciprocal relations similar to Onsager's, revealing a fundamental symmetry in the evolution of statistical systems.

Contribution

It shows that reciprocity in entropic dynamics arises from the geometric structure of the exponential family, extending the principle to a broad class of models.

Findings

Reciprocal relations are derived from information geometric principles.

The symmetry is a general property of entropic dynamics.

The framework connects thermodynamic reciprocity with information theory.

Abstract

Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected values is linear to the gradient of entropy with reciprocal (symmetric) coefficients. Reciprocity principles have been useful in physics since Onsager. Here we show how the entropic dynamics reciprocity is a consequence of the information geometric structure of the exponential family, hence it is a general property that can be extended to a broader class of dynamical models.