Algebraic probability, classical stochastic processes, and counting statistics

TL;DR

This paper establishes a link between algebraic probability and classical stochastic processes, providing a new reformulation that simplifies deriving counting statistics in nonequilibrium physics.

Contribution

It introduces a novel state definition for classical processes within algebraic probability, leading to a straightforward derivation of counting statistics equations.

Findings

Reformulation yields the Doi-Peliti formalism from algebraic probability.

Provides a new derivation method for counting statistics equations.

Connects algebraic probability with classical stochastic process analysis.

Abstract

We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can be reformulated in terms of the algebraic probability. This reformulation immediately gives the Doi-Peliti formalism, which has been frequently used in nonequilibrium physics. As an application of the reformulation, we give a derivation of basic equations for counting statistics, which plays an important role in nonequilibrium physics.