Ensemble Inequivalence in Single Molecule Experiments

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.

Typos in equations fixed. Reference list updated and corrected. Extended

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Cited by in corpus (8)

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• Theory of mechanical unfolding of homopolymer globule: all-or-none transition in force-clamp mode vs phase coexistence in position-clamp mode
• Statistical mechanical model for crack growth
• Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA
• Modeling single-molecule stretching experiments using statistical thermodynamics
• The elasticity of semiflexible polymers with reversible spontaneous curvature in two dimensions