Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport

Abstract

Unlike equilibrium statistical mechanics, with its well-established\nfoundations, a similar widely-accepted framework for non-equilibrium\nstatistical mechanics (NESM) remains elusive. Here, we review some of the many\nrecent activities on NESM, focusing on some of the fundamental issues and\ngeneral aspects. Using the language of stochastic Markov processes, we\nemphasize general properties of the evolution of configurational probabilities,\nas described by master equations. Of particular interest are systems in which\nthe dynamics violate detailed balance, since such systems serve to model a wide\nvariety of phenomena in nature. We next review two distinct approaches for\ninvestigating such problems. One approach focuses on models sufficiently simple\nto allow us to find exact, analytic, non-trivial results. We provide detailed\nmathematical analyses of a one-dimensional continuous-time lattice gas, the\ntotally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic\nmodel for NESM, much like the role the Ising model played for equilibrium\nstatistical mechanics. It is also the starting point for the second approach,\nwhich attempts to include more realistic ingredients in order to be more\napplicable to systems in nature. Restricting ourselves to the area of\nbiophysics and cellular biology, we review a number of models that are relevant\nfor transport phenomena. Successes and limitations of these simple models are\nalso highlighted.\n