title: Reconstructing equilibrium entropy and enthalpy profiles from non-equilibrium pulling.
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.
authors.affiliation: Department of Chemistry, University of California, Irvine, California 92697, USA.
authors.forename: Daun
authors.initials: D
authors.lastname: Jeong
authors.forename: Ioan
authors.initials: I
authors.lastname: Andricioaei
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D019277:Entropy; D008956:Models, Chemical; D008968:Molecular Conformation; D013696:Temperature; D013816:Thermodynamics