David A. Sivak, John D. Chodera, Gavin E. Crooks
Common algorithms for simulating Langevin dynamics are neither microscopically reversible, nor do they preserve the equilibrium distribution. Instead, even with a time-independent Hamiltonian, finite time step Langevin integrators model a driven, nonequilibrium dynamics that breaks time-reversal symmetry. Herein, we demonstrate that these problems can be properly treated with a Langevin integrator that splits the dynamics into separate deterministic and stochastic substeps. This allows the total energy change of a driven system to be divided into heat, work, and shadow work -- the work induced by the finite time step. Through the interpretation of a discrete Langevin integrator as driving the system out of equilibrium, we can bring recent developments in nonequilibrium thermodynamics to bear. In particular, we can invoke nonequilibrium work fluctuation relations to characterize and correct for biases in estimates of equilibrium and nonequilibrium thermodynamic quantities.
View original:
http://arxiv.org/abs/1107.2967
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