A large deviation analysis on the near-equivalence between external and internal reservoirs

João R. Medeirosa, Sílvio M. Duarte Queirós

Resumo


 Within the spirit of van Kampen's \Langevin approach", we discuss the limits of validity of rephrasing the non-equilibrium problem of a particle subject to an external (work)
reservoir | a system where the  uctuation-dissipation is not veried | into the simpler case with an internal (heat) reservoir for which the uctuations and the dissipation arise
from the same source. Using a convenient mapping of the thermomechanical parameters we show that, counter-intuitively, such approach is not only valid for steady state time independent quantities, but also for time dependent thermostatistical quantities, namely
the injected and dissipated uxes. We connect this result with the problem of large devi- ations and conclude that, in this context, we can only distinguish reservoirs by analysingthe \
uctuations of accumulated  uctuations". As a by-product, we learn that the best reference approximation to the large deviation functions of a non-Markovian external reservoir system is not the respective internal reservoir limit | as often assumed and sug-
gested by the Langevin approach | but its internal reservoir analogue system obtained from the mapping of the original thermomechanical parameters.


Texto completo:

PDF

Referências


N.G. van Kampen, Stochastic Processes in Physics and Chemestry, Elsevier, Ams- terdam, 2007.

C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemestry and Natural Sciences, Springer-Verlag, Berlin, 1997.

T. Chou, K. Mallick, R.K.P. Zia, Rep. Prog. Phys. 74 (2011) 116601; U. Seifert, Rep. Prog. Phys. 75 (2012) 126001; R. Klages, W. Just, C. Jarzynski (Eds.), Nonequi-

librium Statistical Physics of Small Systems: Fluctuation Relations and Beyond, Weinheim, Wiley-VCH Verlag, 2013.

H. Nyquist, Phys. Rev. 32 (1928) 110; L. Onsager, Phys. Rev. 37 (1931) 405; R. Kubo, Rep. Prog. Phys. 29 1966 255; U. Marini, B. Marconi, A. Puglisi, L. Rondoni, A. Vulpiani, Phys. Rep. 461 (2008) 111.

H. Mori, Prog. Theo. Phys. 33 (1965) 423; R. Kubo (Ed.), 1965 Tokyo Summer Lectures in Theoretical Physics, New York: Benjamin, 1966.

M.I. Dykman, Phys. Rev. A 42 (1990) 2020.

Several examples can be found in: F. Moss, P.V.E. McClintock (Eds.), Noise in Nonlinear Dynamical Systems (Cambridge, Cambridge University Press, 2009).

D.O. Soares-Pinto, W.A.M. Morgado, Physica A 365 (2006) 289.

P. Lett, R. Short, L. Mandel, Phys. Rev. Lett. 52 (1984) 341; S. Zhu, A.W. Yu, R. Roy, Phys. Rev. A 34 (1986) 4333; R.F. Fox and R. Roy, Phys. Rev. A 35 (1987) 1838; W. Yu, G.P. Agrawal, R. Roy, Opt. Lett. 12 (1987) 806.

K. Vogel, H. Risken, W. Schleich, M. James, F. Moss, P.V.E. McClintock, Phys. Rev. A 35 (1987) 463; K. Vogel, Th. Leiber, H. Risken, P. Hanggi, W. Schleich, Phys. Rev. A 35 (1987) 4882.

F.D. Nobre, A.M.C. Souza, E.M.F Curado, Phy. Rev. E 86 (2012) 061113; E.M.F.Curado, A.M.C. Souza, F.D. Nobre, R.F.S Andrade, Phy. Rev. E 89 (2014) 022117.

W.A.M. Morgado, S.M. Duarte Queiros, D.O. Soares-Pinto, J. Stat. Mech. (2011) P06010; W.A.M. Morgado, T. Guerreiro, Physica A 391 (2012) 3816.

M.I. Dykman, E. Mori, J. Ross, P.M. Hunt, J. Chem. Phys. 100 (1994) 5735; A. Fi- asconaro, B. Spagnolo, Phys. Rev. E 80 (2009) 041110; A.C. Tzemos, D.P.K. Ghikas, Phys. Lett. A 377 (2013) 2307; A. Dechant, E. Lutz, Connecting Active and Passive

Microrheology in Living Cells (2013) Preprint arXiv:1307.6466.

A. Dechant, E. Lutz, D.A. Kessler, E. Barkai, Phys. Rev. X 4 (2014) 011022.

E. Torrontegui, R. Kosloff, Phys. Rev. E 88 (2013) 032103.

A.B. Kolomeisky, J. Phys. Chem. Lett. 2 (2011) 1502.

J. Mehl, B. Lander, C. Bechinger, V. Blickle, U. Seifert Phys. Rev. Lett. 108 (2012)220601

J. Farago, J. Stat. Phys. 107 (2002) 781; J.S. Lee, C. Kwon, H. Park, Phys. Rev. E 87 (2013) 020104(R)


Apontamentos

  • Não há apontamentos.