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

TL;DR

This paper reviews recent developments in non-equilibrium statistical mechanics, emphasizing models with broken detailed balance, including the exactly solvable TASEP and biologically relevant transport models, highlighting their successes and limitations.

Contribution

It provides a comprehensive overview of fundamental issues, mathematical analyses of the TASEP model, and discusses more realistic biological transport models, advancing understanding of NESM.

Findings

TASEP serves as a paradigmatic model for NESM.

Exact solutions for simple non-equilibrium models are achievable.

Biological transport models reveal successes and limitations.

Abstract

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