## The fluctuation theorem as a Gibbs property.(English)Zbl 0941.60099

Let $$\xi\to\varphi(\xi)$$, $$\xi\in\Omega$$, be a smooth discrete-time, reversible dynamical system on a compact, connected manifold $$\Omega$$ and consider the quantity $$N^{-1}\sum^{N/2}_{-N/2} \dot S(\varphi^n(\xi))$$ where $$\dot S$$ is the phase space contraction rate (entropy production rate), i.e. $$\dot S= \log J$$, $$J$$ being the Jacobian corresponding to the dynamics. The fluctuation theorem of Gallavotti and Cohen [Phys. Rev. Lett. 74, 2694-2697 and 80, 931-970] establishes an asymptotic symmetry possessed by the distribution of this quantity under the stationary state of the system. The present paper shows how this property can be understood as a property of Gibbs states once the Gibbs formalism is applied at the level of space-time histories. The connection with the dynamical system comes from the fact that the space-time measure of the system is akin to a Gibbs measure for an interaction determined by the transition probabilities.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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