Information and contact geometric description of expectation variables exactly derived from master equations

TL;DR

This paper introduces a geometric framework combining information and contact geometry to describe the dynamics of expectation variables derived from master equations, revealing exponential convergence and duality properties.

Contribution

It provides a novel geometric approach to analyze expectation variables from master equations using both information and contact geometry, including convergence analysis.

Findings

Expectation variables' dynamics are represented as contact Hamiltonian vector fields.

The convergence rate of the system is exponential.

Duality in information geometry is incorporated into the framework.

Abstract

In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of a set of appropriately chosen Markov kernels. To geometrize such dynamical systems for expectation variables, information geometry is used for expressing equilibrium states, and contact geometry is used for nonequilibrium states. Here time-developments of the expectation variables are identified with contact Hamiltonian vector fields on a contact manifold. Also, it is shown that the convergence rate of this dynamical system is exponential. Duality emphasized in information geometry is also addressed throughout.