Microscopically Reversible Pathways with Memory

Jose Ricardo Arias-Gonzalez

doi:10.3390/math9020127

Abstract

Statistical mechanics is a physics theory that deals with ensembles of microstates of a system compatible with environmental constraints and that on average define a thermodynamic state. The evolution of a small system is normally subjected to changing constraints, as set by a protocol, and involves a stochastic dependence on previous events. Here, we generalize the dynamic trajectories described by a realization of a physical system without dissipation to include those in which the history of previous events is necessary to understand its future. This framework is then used to characterize the processes experienced by the stochastic system, as derived from ensemble averages over the available pathways. We find that the pathways that the system traces in the presence of a protocol entail different statistics from those in its absence and prove that both types of pathways are equivalent in the limit of independent events. Such equivalence implies that a thermodynamic system cannot evolve away from equilibrium in the absence of memory. These results are useful to interpret single-molecule experiments in biophysics and other fields in nanoscience, as well as an adequate platform to describe non-equilibrium processes.

Highlights

Reversibility refers to quasistatic processes that invert isentropically
We have extended thermodynamics to systems that evolve along specific sequences of events driven by changing constraints in the frictionless limit
We have introduced pathway- and protocol-dependent functions, including thermodynamic potentials, that characterize the microstates of the system in the presence of memory

Summary

Introduction

Reversibility refers to quasistatic processes that invert isentropically. Such processes involve a sufficiently slow dynamics to prevent heat flows; more in depth, they take place through a timeless succession of states along which there is no energy dissipation. Protein folding is another in singulo process that showcases the firm link between physical interactions and memory, and how this link brings thermodynamic consequences to the structural and functional fate of a polypeptide [10] Both the synthesis protocol and the amino acid sequence stochastically guide protein folding dynamics through preferential phase-space trajectories [11]. Complete memory effects have been considered in the study of spatial chains made up of physical subunits, including those with symbolic meaning, to access non-equilibrium dynamics [23] and information management in nanoscale systems [24] They have been taken into account to analyze abstract strings of symbols for the paradigm of communication [25]. We end up by illustrating our theory in the context of computing biomolecular systems, where memory effects are inherent to their thermodynamic modeling

Concepts and Terminology

Equilibrium Pathways

Discussion