2007/12/10 by Artur B. Adib · 2 citations
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1021/jp0751458
published as J. Phys. Chem. B 112, 5910 (2008) · 9 pages, 6 figures; in press (J. Phys. Chem. B)
arxiv created 2007/12/10 · arxiv updated 2009/12/01
In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requiring the evaluation of the second derivative of the potential in addition to the force. Here it is argued that both actions are equivalent prescriptions for the purposes of reweighting and sampling trajectories, whereas the most probable path is more generally given by the global minimum of the action involving the second derivative term. The answer to this apparent paradox lies in the non-differentiable character of Brownian paths, as well as in the "entropy" associated with a given trajectory.