Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale

Details Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale

2010-09-03

arxiv.org/abs/1009.0707v2

J Stat Phys 143, 543 (2011)

Physics

Condensed Matter

Statistical Mechanics

41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions, new results in Section 6

Scientific paper

In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.

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