Rényi Entropy of the Totally Asymmetric Exclusion Process

I will present our analytic work on the totally asymmetric exclusion process (TASEP), where we have calculated a measure known as the Rényi entropy. This is a generalisation of the more common Shannon entropy, that has a neat interpretation for equilibrium systems. Away from equilibrium (the case for any real system e.g. biological processes), a physical interpretation remains elusive. However, we suspect the nonanalyticities of a given system’s Rényi entropy may serve as an indicator as to whether a system is in or out of equilibrium.

In order to calculate this entropy, we map configurations in the TASEP (that has a probability distribution with a combinatorial-like structure, in contrast with the usual equilibrium Boltzmann weights) to a problem involving a biased discrete 2D random walk, which we make a generalisation to in order to analytically explore the entropy in different phases. Importantly, we find a different structure to what one would find at equilibrium, suggesting an inherent difference between the probability distributions of systems in and out of equilibrium.