The European Physical Journal Special Topics

, Volume 226, Issue 10, pp 2299–2310

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

  • Massimiliano Giona
  • Antonio Brasiello
  • Silvestro Crescitelli
Regular Article
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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Copyright information

© 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 RomaRomaItaly
  2. 2.Dipartimento di Ingegneria Industriale Università degli Studi di SalernoFisciano (SA)Italy
  3. 3.Dipartimento di Ingegneria Chimica dei Materiali e della Produzione Industriale Università degli Studi di Napoli “Federico II”NapoliItaly

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