Kac limit and thermodynamic characterization of stochastic dynamics driven by Poisson-Kac fluctuations
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- Giona, M., Brasiello, A. & Crescitelli, S. Eur. Phys. J. Spec. Top. (2017). doi:10.1140/epjst/e2017-70010-6
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We analyze the thermodynamic properties of stochastic differential equations driven by smooth Poisson-Kac fluctuations, and their convergence, in the Kac limit, towards Wiener-driven Langevin equations. Using a Markovian embedding of the stochastic work variable, it is proved that the Kac-limit convergence implies a Stratonovich formulation of the limit Langevin equations, in accordance with the Wong-Zakai theorem. Exact moment analysis applied to the case of a purely frictional system shows the occurrence of different regimes and crossover phenomena in the parameter space.