Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes |
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Authors: | A. Faggionato D. Gabrielli M. Ribezzi Crivellari |
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Affiliation: | 1.Dipartimento di Matematica “G. Castelnuovo”,Università “La Sapienza”,Rome,Italy;2.Dipartimento di Matematica,Università dell’Aquila,L’Aquila,Italy;3.Dipartimento di Fisica,Università Roma Tre,Rome,Italy |
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Abstract: | We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x,σ)∈Ω×Γ, Ω being a region in ℝ d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at , 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry relation with involution map different from time-reversal. |
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