Capturing the local entropy production of an active Brownian particles system by compression

The entropy production of a stationary process is known to be the Kullback-Leibler divergence (KLD), or relative entropy, between the probability of observing a trajectory with time running forward and its time reversal, which quantitatively characterizes the time-reversal asymmetry and features the nonequilibrium nature of the system. Here we use a compression based Ziv-Merhav method and other techniques to estimate KLD and time reversal symmetry to define a natural spatial decomposition of entropy production by applying the algorithms on discrete time series of state evolution in local block regions. As an example, we will discuss how local entropy production is captured with this method in a phase-separated system of active Brownian particles.