Variational principle of counting statistics in master equations
Abstract
We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the similar path integral formulation without the assumption of mesoscopic systems. It has been clarified that the saddle point method for the path integral is not an approximation, but a valid procedure in the present derivation. Hence, a variational principle in the counting statistics is naturally derived. In order to obtain the variational principle, we employ many independent replicas of the same system. In addition, the Euler-Maclaurin formula is used in order to connect the discrete and continuous properties of the system.
Cite
@article{arxiv.0906.5187,
title = {Variational principle of counting statistics in master equations},
author = {Jun Ohkubo},
journal= {arXiv preprint arXiv:0906.5187},
year = {2009}
}
Comments
4 pages, no figure