Non-equilibrium thermodynamics of piecewise deterministic markov processes

Journal of Statistical Physics

Volumn 137, Issue 2, 2009, Pages 259-304

  Faggionato, A ^a   Gabrielli, D ^b   Crivellari, M Ribezzi ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c ROMA TRE UNIVERSITY   (Italy)

Author keywords

Large deviations; Non equilibrium processes; Piecewise deterministic Markov processes; Stationary states

Indexed keywords

EID: 76149119409     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9850-x     Document Type: Article

References (23)

1. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Fluctuations in stationary nonequilibrium states of irreversible processes. Phys. Rev. Lett. 87, 040601 (2001); 4 pp.
2. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Macroscopic fluctuation theory for stationary non-equilibrium states. J. Stat. Phys. 107(3-4), 635-675 (2002).
3. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Large deviations for the boundary driven symmetric simple exclusion process. Math. Phys. Anal. Geom. 6(3), 231-267 (2003).
4. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Stochastic interacting particle systems out of equilibrium. J. Stat. Mech. P07014 (2007).
5. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems. Preprint available online at http://www. arxiv. org/abs/0807. 4457 (2008).
6. Billingsley, P.: Convergence of Probability Measures, 2nd edn. Wiley, New York (1999).
7. Breitung, K. W.: Asymptotic Approximations for Probability Integrals. Lecture Notes in Mathematics, vol. 1592. Springer, Berlin (1994).
8. Cassandras, C. G., Lygeros, J. (eds.): Stochastic Hybrid Systems. CRC Press, Boca Raton (2006).
9. Davis, M. H. A.: Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models (with discussion). J. R. Stat. Soc. B 46, 353-388 (1984).
10. Davis, M. H. A.: Markov Models and Optimization. Monographs on Statistics and Applied Probability, vol. 49. Chapman and Hall, London (1993).
11. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Applications of Mathematics, vol. 38. Springer, Berlin (1998).
12. Faggionato, A., Gabrielli, D., Ribezzi Crivellari, M.: Averaging and large deviation principles for fully-coupled piecewise deterministic Markov processes and applications to molecular motors. Preprint available online at http://www. arxiv. org/abs/0808. 1910 (2008).
13. Faggionato, A., Gabrielli, D., Ribezzi Crivellari, M.: In preparation.
14. Freidlin, M. I., Wentzell, A. D.: Random Perturbations of Dynamical Systems. Grundlehren der mathematichen Wissenschaften, vol. 260. Springer, Berlin (1984).
15. Jülicher, F., Ajdari, A., Prost, J.: Modelling molecular motors. Rev. Mod. Phys. 69, 1269 (1997).
16. Kipnis, C., Landim, C.: Scaling Limits of Interacting Particle Systems. Springer, Berlin (1999).
17. Kurchan, J.: Fluctuation theorem for stochastic dynamics. J. Phys. A Math. Gen. 31, 3719-3729 (1998).
18. Lebowitz, J. L., Spohn, H.: A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics. J. Stat. Phys. 95, 333-365 (1999).
19. Maes, C.: The fluctuation theorem as a Gibbs property. J. Stat. Phys. 95(1/2), 367-392 (1999).
20. Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361, 57-265 (2002).
21. Ribezzi Crivellari, M.: Graduate Thesis, Department of Physics, University "La Sapienza", Rome (2007).
22. Vilfan, A., Duke, T.: Instabilities in the transient response of muscle. Biophys. J. 85, 818-826 (2003).
23. Vilfan, A., Frey, E., Schwabl, F.: Force-velocity relations of a two state crossbridge model for molecular motors. Europhys. Lett. 45, 283-289 (1999).