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

  • Massimiliano Giona
  • Antonio Brasiello
  • Silvestro Crescitelli
Regular Article

DOI: 10.1140/epjst/e2017-70010-6

Cite this article as:
Giona, M., Brasiello, A. & Crescitelli, S. Eur. Phys. J. Spec. Top. (2017). doi:10.1140/epjst/e2017-70010-6
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Part of the following topical collections:
  1. Aspects of Statistical Mechanics and Dynamical Complexity

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.

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© EDP Sciences and Springer 2017

Authors and Affiliations

  • Massimiliano Giona
    • 1
  • Antonio Brasiello
    • 2
  • Silvestro Crescitelli
    • 3
  1. 1.Dipartimento di Ingegneria Chimica DICMA Facoltà di Ingegneria, La Sapienza Università di Roma via Eudossiana 18RomaItaly
  2. 2.Dipartimento di Ingegneria Industriale Università degli Studi di Salerno via Giovanni Paolo II 132Fisciano (SA)Italy
  3. 3.Dipartimento di Ingegneria Chimica dei Materiali e della Produzione Industriale Università degli Studi di NapoliNapoliItaly

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