Emergence of effective temperatures in an out-of-equilibrium model of biopolymer folding

TL;DR

This study explores how effective temperatures can be defined and distinguished in an out-of-equilibrium RNA folding model under external forces, revealing different temperature concepts linked to system relaxation and heat exchange.

Contribution

It introduces and compares two types of effective temperatures in a stochastic RNA folding model, extending the understanding of thermodynamic concepts out of equilibrium.

Findings

Multiple effective temperatures can be defined depending on the observable.

The fluctuation-dissipation relation temperature depends on slow relaxation times.

A kinetic temperature based on heat exchange is valid at any external force frequency.

Abstract

We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA/protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly-interacting thermal bath. Notably, this 'kinetic' temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple 4-state Markov model which describes the long-time behaviour of the RNA molecule.