Reconstructing Equilibrium Entropy and Enthalpy Profiles from Non-equilibrium Pulling

TL;DR

This paper develops exact analytical methods to derive equilibrium entropy and internal energy profiles from non-equilibrium pulling trajectories using the Jarzynski identity and stochastic path integrals, enabling detailed thermodynamic analysis without repeated measurements.

Contribution

It introduces three novel analytical formulas for decomposing free energy profiles into entropy and energy from non-equilibrium data, advancing thermodynamic analysis in single-molecule experiments.

Findings

Derived exact formulas for temperature derivatives of free energy profiles.

Presented three analytical methods for entropy-energy decomposition.

Validated methods with Langevin simulations of biomolecular models.

Abstract

The Jarzynski identity can be applied to instances when a microscopic system is pulled repeatedly but quickly along some coordinate, allowing the calculation of an equilibrium free energy profile along the pulling coordinate from a set of independent non-equilibrium trajectories. Using the formalism of Wiener stochastic path integrals in which we assign temperature-dependent weights to Langevin trajectories, we derive exact formulae for the temperature derivatives of the free energy profile. This leads naturally to analytical expressions for decomposing a free energy profile into equilibrium entropy and internal energy profiles from non-equilibrium pulling. This decomposition can be done from trajectories evolved at a unique temperature without repeating the measurement as done in finite-difference decompositions. Three distinct analytical expressions for the entropy-energy decomposition are derived: using a time-dependent generalization of the weighted histogram analysis method, a quasi harmonic spring limit, and a Feynman-Kac formula. The three novel formulae of reconstructing the pair of entropy-energy profiles are exemplified by Langevin simulations of a two-dimensional model system prototypical for force-induced biomolecular conformational changes. Connections to single-molecule experimental means to probe the functionals needed in the decomposition are suggested.