Fluctuation theorems for non-Markovian quantum processes

Abstract

Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical-like non-Markovian stochastic unravelling, which is demonstrated to lead to a correction of the standard entropic fluctuation theorem. This correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system: Due to memory effects single realizations of a dynamical process are no longer independent, and their correlations fundamentally affect the behavior of entropy fluctuations.

Nonequilibrium quantum fluctuations of work

“…Also, in certain cases of p kl < 0 we can follow the reasoning of (29) and still define positive probabilities by coarse-graining p kl .…”

“…Time-global definitions look for the work done between two moments of time, as usual for any transfer quantity [10][11][12][13][14][15][16][17][18][19][20][21]. Timelocal approaches adapt the global definitions infinitesimally along an effective quantum trajectory [22][23][24][25][26][27][28][29][30][31][32].…”

Thermodynamics of quantum-jump-conditioned feedback control

“…Using W delay (0) from Eqs. (36) and (37) we can calculate the steady state probabilities p 0 (τ α ),p 1 (τ α ) for arbitrary delay times τ α . They are unique in this model.…”

Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system

“…For such systems a detailed understanding of the memory effects is desirable. The study of non-Markovianity in open quantum systems has become a subject of broad interest in recent years due to the rapid development in quantum information [5,6] and in quantum thermodynamics [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. There is a great variety of nonMarkovianity measures for open quantum systems proposed in the literature [22][23][24][25][26][27][28][29][30], which are not identical.…”