Stochastic actions for diffusive dynamics: Reweighting, sampling, and minimization

Abstract

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.

9 pages, 6 figures; in press (J. Phys. Chem. B)

References in corpus (4)

• Dominant Pathways in Protein Folding
• Efficient Dynamic Importance Sampling of Rare Events in One Dimension
• Sampling diffusive transition paths
• Computing probabilities of very rare events for Langevin processes: a new method based on importance sampling

Cited by in corpus (24)

• Uncertainty relations in stochastic processes: An information inequality approach
• Dominant Reaction Pathways in High Dimensional Systems
• Summing over trajectories of stochastic dynamics with multiplicative noise
• Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways
• Path integral analysis of Jarzynski's equality: Analytical results
• Path Weight Sampling: Exact Monte Carlo Computation of the Mutual Information between Stochastic Trajectories
• Path probability ratios for Langevin dynamics -- exact and approximate
• An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations
• Experimental measurement of relative path probabilities and stochastic actions
• Most probable path of an active Brownian particle
• Simulating Stochastic Dynamics Using Large Time Steps
• Stochastic action for tubes: Connecting path probabilities to measurement
• Molecular Dynamics at Low Time Resolution
• Appearance of Thermal Time
• Time-Slicing Path-integral in Curved Space
• Quantum Charge Transport and Conformational Dynamics of Macromolecules
• Reconstructing Equilibrium Entropy and Enthalpy Profiles from Non-equilibrium Pulling
• Trajectory reweighting for non-equilibrium steady states
• Time-Asymmetric Fluctuation Theorem and Efficient Free Energy Estimation
• Most probable paths for active Ornstein-Uhlenbeck particles
• Inferring nonlinear fractional diffusion processes from single trajectories
• Irreversibility of stochastic state transitions in Langevin systems with odd elasticity
• Timescales for stochastic barrier crossing: inferring the potential from nonequilibrium data
• Sojourn probabilities in tubes and pathwise irreversibility for Itô processes