On Quantum Fluctuation Theorem

Since the numerical study by Evans et al. in 1993, fluctuation theorem (FT) (a symmetry for the fluctuation of the entropy production) has been theoretically well investigated, such as the steady state of Nose\' -Hoover systems, Anosov-like dynamical systems, and Markovian stochastic dynamics.And it is well understood that as special cases, FT includes the 2nd-law of thermodynamics and the linear-response theory.It seems widely accepted that under the local-detailed-balance condition[1,2], the FT for classical stochastic systems does hold.
On the contrary, the local-detailed-balance condition can not directly apply to quantum systems, since the measurements affect the dynamics.With the aid of the diagonalizing basis, we can obtain the trajectory-picture and utilize the detailed balance relation within the master equation[4], but this approach does not include the measurement.
In this seminar, at first we will investigate the underlying local-detailed-balance condition for open quantum system such as Langevin systems[3] and discuss about the definition of entropy production.Secondly the non-Gaussian-fluctuation of entropy production is analytically derived as well as the derivation of FT for time-dependent linear Ford-Kac-Mazur model[5].We will also show that distribution of such a non-Gaussian-fluctuation approaches to the spectral distribution for the work externally done in classical limit.

[1] G. E. Crooks, Phys. Rev. E 61, 2361-2366 (2000)
[2] J. L. Lebowitz and H.Spohn, J. Stat. Phys. 95, 333--366, (1999)
[3] T. Monnai, Phys. Rev. E 72, 027102 (2005)
[4] M. Esposito, and S. Mukamel, Phys. Rev. E 73, 046129 (2006)
[5] T. Monnai, Proceedings of the 6th International Summer School/Conference "Let's face chaos through nonlinear dynamics" (in press)