Stochastic thermodynamic interpretation of information geometry

TL;DR

This paper establishes a novel connection between stochastic thermodynamics and information geometry, deriving an inequality that links system speed and thermodynamic cost, with applications to biochemical enzyme reactions.

Contribution

It introduces a new link between stochastic thermodynamics and information geometry, leading to an information geometric inequality interpreted as a thermodynamic uncertainty relation.

Findings

Derived an information geometric inequality as a thermodynamic uncertainty relation.

Numerically applied the inequality to a biochemical enzyme reaction model.

Demonstrated the relevance of information geometry in non-stationary thermodynamic systems.

Abstract

In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand non-stationary dynamics of systems far from equilibrium. In this letter, we have found a new link between stochastic thermodynamics and information theory well known as information geometry. By applying this link, an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost. We have numerically applied an information geometric inequality to a thermodynamic model of biochemical enzyme reaction.