Ensemble Inequivalence in Single Molecule Experiments

TL;DR

This paper investigates the conditions under which different statistical ensembles become equivalent in single molecule experiments, revealing that ensemble inequivalence persists in certain regimes and characterizing the transition to equivalence.

Contribution

It provides a detailed analysis of ensemble differences in single polymer chains, highlighting the scaling behavior and conditions for ensemble equivalence or inequivalence.

Findings

Ensemble inequivalence persists in low-force regimes for long chains.

The transition from inequivalence to equivalence depends on chain length and force.

Scaling laws describe how ensemble differences diminish with increasing chain length.

Abstract

In bulk systems the calculation of the main thermodynamic quantities leads to the same expectation values in the thermodynamic limit, regardless of the choice of the statistical ensemble. Single linear molecules can be still regarded as statistical systems, where the thermodynamic limit is represented by infinitely long chains. The question of equivalence between different ensembles is not at all obvious and has been addressed in the literature, with sometimes contradicting conclusions. We address this problem by studying the scaling properties of the ensemble difference for two different chain models, as a function of the degree of polymerization. By characterizing the scaling behavior of the difference between the isotensional (Gibbs) and isometric (Helmholtz) ensembles in the transition from the low-stretching to the high-stretching regime, we show that ensemble equivalence cannot be reached for macroscopic chains in the low force regime, and we characterize the transition from the inequivalence to the equivalence regime.