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

Abstract

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 onedimensional 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.

New Model for Understanding Mechanisms of Biological Signaling: Direct Transport via Cytonemes

“…The steady-state properties for the TASEP on finite lattice segments with open boundaries have been calculated exactly. 31,32 The particle flux through the segment of length n is given by, 31…”

Fluctuations and correlations of a driven tracer in a hard-core lattice gas

“…In the absence of external driving and when additional adsorption/desorption processes with a reservoir of particles are considered, it corresponds to the so-called dynamical percolation [12,13]. Last, in the case of a constant external forcing experienced by all the particles, it identifies with the asymmetric exclusion process, which has now become a paradigmatic model, both in the absence (see [14] for a recent review) or in the presence [15] of adsorption/desorption processes. This model of driven tracer diffusion has been investigated both in the physical [16][17][18][19][20] and in the mathematical [21,22] literatures.…”

Proceedings of the Asia-Pacific Econophysics Conference 2016 — Big Data Analysis and Modeling toward Super Smart Society — (APEC-SSS2016)

“…An exclusion rule prevents two particles to be on the same site, so that a particle is allowed to hop only if the site in front is empty. This model is called TASEP (Totally Asymmetric Simple Exclusion Process) and is shown to have a phase transition from a free flow phase to a jammed phase when the density increases [9][10][11][12]. It can be seen as a simplified version of more realistic models based on cellular automata for traffic simulation [13].…”