Eur. Phys. J. Special Topics © EDP Sciences, Springer-Verlag 2017 DOI: 10.1140/epjst/e2017-70010-6 T HE EUROPEAN P HYSICAL JOURNAL SPECIAL TOPICS Regular Article Kac limit and thermodynamic characterization of stochastic dynamics driven by Poisson-Kac fluctuations Massimiliano Giona 1, a , Antonio Brasiello 2 , and Silvestro Crescitelli 3 1 Dipartimento di Ingegneria Chimica DICMA Facolt` a di Ingegneria, La Sapienza Universit` a di Roma via Eudossiana 18, 00184, Roma, Italy 2 Dipartimento di Ingegneria Industriale Universit` a degli Studi di Salerno via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy 3 Dipartimento di Ingegneria Chimica dei Materiali e della Produzione Industriale Universit` a degli Studi di Napoli “Federico II” piazzale Tecchio 80, 80125 Napoli, Italy Received 12 January 2017 Published online 16 February 2017 Abstract. We analyze the thermodynamic properties of stochastic dif- ferential 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 vari- able, 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. 1 Introduction Stochastic models of microdynamics play a central role in statistical physics with broad applications in polymer and colloidal sciences [1, 2]. An important field of re- search is related to the thermodynamic analysis of these systems, with particular attention on fluctuation-dissipation properties and large-deviation results [3–5]. The overwhelming majority of stochastic approaches are grounded on the Langevin-Wiener paradigm. Within this paradigm, the equations of motion are writ- ten in the form of a stochastic Langevin equation in which the stochastic forcing term is proportional to the increments of a Wiener process. The assumption of Wiener per- turbations stems from a large-number ansatz, typical of many models adopted in sta- tistical physics. In these models the fluctuating term accounts for a manifold of small random contributions, the superposition of which possesses independent increments distributed in a Gaussian way. One of the main consequences of this assumption is that the trajectories of Wiener processes are, with probability 1, nowhere differen- tiable fractal curves possessing a Hausdorff dimension d H =3/2[6]. Another approach to the modelling of stochastic fluctuations, alternative to the Wiener paradigm, is based on almost everywhere (a.e.) differentiable stochastic a e-mail: massimiliano.giona@uniroma1.it