1201.5613 (Édgar Roldán et al.)

Entropy production and Kullback-Leibler divergence between stationary
trajectories of discrete systems    [PDF]

Édgar Roldán, Juan M. R. Parrondo

The irreversibility of a stationary time series can be quantified using the
Kullback-Leibler divergence (KLD) between the probability to observe the series
and the probability to observe the time-reversed series. Moreover, this KLD is
a tool to estimate entropy production from stationary trajectories since it
gives a lower bound to the entropy production of the physical process
generating the series. In this paper we introduce analytical and numerical
techniques to estimate the KLD between time series generated by several
stochastic dynamics with a finite number of states. We examine the accuracy of
our estimators for a specific example, a discrete flashing ratchet, and
investigate how close is the KLD to the entropy production depending on the
number of degrees of freedom of the system that are sampled in the
trajectories.

View original: http://arxiv.org/abs/1201.5613