Fluctuation theorems from non-equilibrium Onsager-Machlup theory for a Brownian particle in a time-dependent harmonic potential

Roberto Deza 1 , Gonzalo Izús 1 , and Horacio Wio 2
  • 1 IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, 7600, Mar del Plata, Argentina
  • 2 IFCA (Universidad de Cantabria and CSIC), Av. de los Castros s/n, E-39005, Santander, Spain

Abstract

We discuss the case of a Brownian particle which is harmonically bound and multiplicatively forced-namely bound by V(x,t)=1/2 a(t)x 2 where a(t)is externally controlled-as another instance that provides a generalization of Onsager-Machlup’s theory to non-equilibrium states, thus allowing establishment of several fluctuation theorems. In particular, we outline the derivation of a fluctuation theorem for work, through the calculation of the work probability distribution as a functional integral over stochastic trajectories.

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  • [1] J. García-Ojalvo, J. M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999) http://dx.doi.org/10.1007/978-1-4612-1536-3

  • [2] F. Sagués, J. M. Sancho, J. García-Ojalvo, Rev. Mod. Phys. 79, 829 (2007) http://dx.doi.org/10.1103/RevModPhys.79.829

  • [3] H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edition (Wiley, NY, 1985)

  • [4] C. Jarzynski, Eur. Phys. J. B 64, 331 (2008) http://dx.doi.org/10.1140/epjb/e2008-00254-2

  • [5] D. J. Evans, D. J. Searles, Adv. Phys. 51, 1529 (2002) http://dx.doi.org/10.1080/00018730210155133

  • [6] V. Y. Chernyak, M. Chertkov, C. Jarzynski, J. Stat. Mech., P08001 (2006)

  • [7] D. M. Carberry et al., Phys. Rev. Lett. 92, 140601 (2004)

  • [8] S. Schuler, T. Speck, C. Tietz, J. Wrachtrup, U. Seifert, Phys. Rev. Lett. 94, 180602 (2005)

  • [9] N. C. Harris, Y. Song, C.-H. Kiang, Phys. Rev. Lett. 99, 068101 (2007)

  • [10] T. Taniguchi, E. G. D. Cohen, J. Stat. Phys. 126, 1 (2007) http://dx.doi.org/10.1007/s10955-006-9252-2

  • [11] N. Singh, J. Stat. Phys. 131, 405 (2008) http://dx.doi.org/10.1007/s10955-008-9503-5

  • [12] C. D. Batista, G. Drazer, D. Reidel, H. S. Wio, Phys. Rev. E 54, 86 (1996) http://dx.doi.org/10.1103/PhysRevE.54.86

  • [13] G. G. Izús, R. R. Deza, H. S. Wio (2008) (in preparation)

  • [14] H. S. Wio, C. Budde, C. Briozzo, P. Colet, Int. J. Mod. Phys. B 6, 679 (1995) http://dx.doi.org/10.1142/S0217979295000252

  • [15] D. E. Strier, G. Drazer, and H. S. Wio, Physica A 283, 255 (2000) http://dx.doi.org/10.1016/S0378-4371(00)00163-1

  • [16] J. A. Giampaoli, D. E. Strier, C. D. Batista, G. Drazer, H. S. Wio, Phys. Rev. E 60, 2540 (1999) http://dx.doi.org/10.1103/PhysRevE.60.2540

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