An Introduction to the Non-Equilibrium Steady States of Maximum Entropy Spike Trains

Abstract

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the literature of non-equilibrium statistical mechanics. This tutorial provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics.

Keywords

• non-equilibrium steady states
• maximum entropy principle
• spike train statistics
• entropy production