Monotonicity of the dynamical activity

Details Monotonicity of the dynamical activity Monotonicity of the dynamical activity

2011-02-14

arxiv.org/abs/1102.2690v2

Physics

Mathematical Physics

18 pages, 1 figure; v2: extended with examples and more detailed proofs

Scientific paper

We prove that the Donsker-Varadhan large deviation functional for the occupations in a finite Markov jump process is monotone under the Master equation evolution. This functional is non-entropic when the system is driven away from detailed balance; it rather measures an excess in time-symmetric dynamical activity. Our proof of monotone behavior works under two conditions: (1) the initial distribution is close enough to stationarity, or equivalently for our context, we look at large times with respect to the relaxation time, and (2) a certain spectral sector-condition equivalent to "normal" linear-response behavior is satisfied.

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