Algebraic Probability, Classical Stochastic Processes, and Counting Statistics

Abstract

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