1,905 research outputs found
Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy Estimates II. A Feynman-Kac Formalism
The nonequilibrium fluctuation theorems have paved the way for estimating
equilibrium thermodynamic properties, such as free energy differences, using
trajectories from driven nonequilibrium processes. While many statistical
estimators may be derived from these identities, some are more efficient than
others. It has recently been suggested that trajectories sampled using a
particular time-dependent protocol for perturbing the Hamiltonian may be
analyzed with another one. Choosing an analysis protocol based on the
nonequilibrium density was empirically demonstrated to reduce the variance and
bias of free energy estimates. Here, we present an alternate mathematical
formalism for protocol postprocessing based on the Feynmac-Kac theorem. The
estimator that results from this formalism is demonstrated on a few
low-dimensional model systems. It is found to have reduced bias compared to
both the standard form of Jarzynski's equality and the previous protocol
postprocessing formalism.Comment: 21 pages, 5 figure
Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy Estimates
When a system is driven out of equilibrium by a time-dependent protocol that
modifies the Hamiltonian, it follows a nonequilibrium path. Samples of these
paths can be used in nonequilibrium work theorems to estimate equilibrium
quantities, such as free energy differences. Here, we consider analyzing paths
generated with one protocol using another one. It is posited that analysis
protocols which minimize the lag, the difference between the nonequilibrium and
the instantaneous equilibrium densities, will reduce the dissipation of
reprocessed trajectories and lead to better free energy estimates. Indeed, when
minimal lag analysis protocols based on exactly soluble propagators or relative
entropies are applied to several test cases, substantial gains in the accuracy
and precision of estimated free energy differences are observed.Comment: 12 pages, 6 figures. Expanded and clarified from original version. To
appear in J. Chem. Phy
Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation
Metropolis Monte Carlo simulation is a powerful tool for studying the
equilibrium properties of matter. In complex condensed-phase systems, however,
it is difficult to design Monte Carlo moves with high acceptance probabilities
that also rapidly sample uncorrelated configurations. Here, we introduce a new
class of moves based on nonequilibrium dynamics: candidate configurations are
generated through a finite-time process in which a system is actively driven
out of equilibrium, and accepted with criteria that preserve the equilibrium
distribution. The acceptance rule is similar to the Metropolis acceptance
probability, but related to the nonequilibrium work rather than the
instantaneous energy difference. Our method is applicable to sampling from both
a single thermodynamic state or a mixture of thermodynamic states, and allows
both coordinates and thermodynamic parameters to be driven in nonequilibrium
proposals. While generating finite-time switching trajectories incurs an
additional cost, driving some degrees of freedom while allowing others to
evolve naturally can lead to large enhancements in acceptance probabilities,
greatly reducing structural correlation times. Using nonequilibrium driven
processes vastly expands the repertoire of useful Monte Carlo proposals in
simulations of dense solvated systems
Initial correlations in nonequilibrium Falicov-Kimball model
The Keldysh boundary problem in a nonequilibrium Falicov-Kimball model in
infinite dimensions is studied within the truncated and self-consistent
perturbation theories, and the dynamical mean-field theory. Within the model
the system is started in equilibrium, and later a uniform electric field is
turned on. The Kadanoff-Baym-Wagner equations for the nonequilibrium Green
functions are derived, and numerically solved. The contributions of initial
correlations are studied by monitoring the system evolution. It is found that
the initial correlations are essential for establishing full electron
correlations of the system and independent on the starting time of preparing
the system in equilibrium. By examining the contributions of the initial
correlations to the electric current and the double occupation, we find that
the contributions are small in relation to the total value of those physical
quantities when the interaction is weak, and significantly increase when the
interaction is strong. The neglect of initial correlations may cause artifacts
in the nonequilibrium properties of the system, especially in the strong
interaction case
Path integral analysis of Jarzynski's equality: Analytical results
We apply path integrals to study nonequilibrium work theorems in the context
of Brownian dynamics, deriving in particular the equations of motion governing
the most typical and most dominant trajectories. For the analytically soluble
cases of a moving harmonic potential and a harmonic oscillator with
time-dependent natural frequency, we find such trajectories, evaluate the
work-weighted propagators, and validate Jarzynski's equality.Comment: 10 pages, 1 figur
- …