Daun Jeong, Ioan Andricioaei
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. By performing this calculation at different temperatures, derivatives of the free energy can in principle be obtained by finite difference. Here we show that, by applying a trajectory reweighting formalism for Langevin dynamics, temperature-derivatives of the free energy can also be recovered exactly at slightly perturbed temperatures but sending the perturbation to zero analytically, and thus without repeating the measurement. This technique can be used to derive exact analytical expressions for the equilibrium entropy and internal energy profiles along the pulling coordinate via standard thermodynamic identities involving temperature derivatives of the free energy. The novel method of reconstructing these profiles is exemplified on a prototypical model system.
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http://arxiv.org/abs/1210.5793
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