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The Jarzynski identity can be applied to instances when a microscopic systemis pulled repeatedly but quickly along some coordinate, allowing thecalculation of an equilibrium free energy profile along the pulling coordinatefrom a set of independent non-equilibrium trajectories. Using the formalism ofWiener stochastic path integrals in which we assign temperature-dependentweights to Langevin trajectories, we derive exact formulae for the temperaturederivatives of the free energy profile. This leads naturally to analyticalexpressions for decomposing a free energy profile into equilibrium entropy andinternal energy profiles from non-equilibrium pulling. This decomposition canbe done from trajectories evolved at a unique temperature without repeating themeasurement as done in finite-difference decompositions. Three distinctanalytical expressions for the entropy-energy decomposition are derived: usinga time-dependent generalization of the weighted histogram analysis method, aquasi harmonic spring limit, and a Feynman-Kac formula. The three novelformulae of reconstructing the pair of entropy-energy profiles are exemplifiedby Langevin simulations of a two-dimensional model system prototypical forforce-induced biomolecular conformational changes. Connections tosingle-molecule experimental means to probe the functionals needed in thedecomposition are suggested.

Reconstructing Equilibrium Entropy and Enthalpy Profiles from Non-equilibrium Pulling