Algebraic probability, classical stochastic processes, and counting statistics

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.

10 pages

References in corpus (2)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• One-parameter extension of the Doi-Peliti formalism and relation with orthogonal polynomials

Cited by in corpus (11)

• Extended duality relations between birth-death processes and partial differential equations
• On dualities for SSEP and ASEP with open boundary conditions
• Quantifying Rare Events in Stochastic Reaction-Diffusion Dynamics Using Tensor Networks
• Lie algebraic discussions for time-inhomogeneous linear birth-death processes with immigration
• Doi-Peliti Path Integral Methods for Stochastic Systems with Partial Exclusion
• Karlin-McGregor-like formula in a simple time-inhomogeneous birth-death process
• Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes
• Duality relations between spatial birth-death processes and diffusions in Hilbert space
• Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes
• Duality-based calculations for transition probabilities in stochastic chemical reactions
• Time Series Path Integral Expansions for Stochastic Processes