Crowding breaks the forward/backward symmetry of transition times in biased random walks

TL;DR

This paper investigates how crowding and non-equilibrium conditions in biased random walks cause asymmetry in forward and backward transition times, revealing underlying microscopic features of complex systems.

Contribution

It provides an exact analysis of symmetry breaking in transition times using solvable stochastic models, highlighting factors like crowding and measurement methods.

Findings

Asymmetry depends on deviation from equilibrium

Crowding influences transition time asymmetry

Measurement methods affect observed asymmetry

Abstract

Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and provide a clear physical picture. Recent theoretical studies made a surprising discovery that in complex systems the symmetry of molecular forward/backward transition times with respect to local bias in the dynamics may be broken and it may take longer to go downhill than uphill. The physical origins of these phenomena remain not fully understood. Here we explore in more detail the microscopic features of the symmetry breaking in the forward/backward transition times by analyzing exactly solvable discrete-state stochastic models. In particular, we consider a specific case of two random walkers on four-sites periodic lattice as the way to represent the general systems with multiple pathways. It is found that the asymmetry in transition times depends on several factors that include the degree of deviation from equilibrium, the particle crowding and methods of measurements of dynamic properties. Our theoretical analysis suggests that the asymmetry in transition times can be explored experimentally for determining the important microscopic features of natural processes by quantitative measuring the local deviations from equilibrium and the degrees of crowding.