Eur. Phys. J. Special Topics 226, 2299-2310 (2017)
https://doi.org/10.1140/epjst/e2017-70010-6

Regular Article

Kac limit and thermodynamic characterization of stochastic dynamics driven by Poisson-Kac fluctuations

¹ Dipartimento di Ingegneria Chimica DICMA Facoltà di Ingegneria, La Sapienza Università di Roma via Eudossiana 18, 00184, Roma, Italy
² Dipartimento di Ingegneria Industriale Università degli Studi di Salerno via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
³ Dipartimento di Ingegneria Chimica dei Materiali e della Produzione Industriale Università degli Studi di Napoli “Federico II” piazzale Tecchio 80, 80125 Napoli, Italy

^a e-mail: massimiliano.giona@uniroma1.it

Received: 12 January 2017
Published online: 16 February 2017

Abstract

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.