Algebraic Probability, Classical Stochastic Processes, and Counting Statistics

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...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2013-08, Vol.82 (8), p.084001-084001-7
Main Author: Ohkubo, Jun
Format: Article
Language:English
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Summary: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.
ISSN:0031-9015
1347-4073
DOI:10.7566/JPSJ.82.084001