390 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
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
Optimized free energies from bidirectional single-molecule force spectroscopy
An optimized method for estimating path-ensemble averages using data from
processes driven in opposite directions is presented. Based on this estimator,
bidirectional expressions for reconstructing free energies and potentials of
mean force from single-molecule force spectroscopy - valid for biasing
potentials of arbitrary stiffness - are developed. Numerical simulations on a
model potential indicate that these methods perform better than unidirectional
strategies.Comment: 4 pages, 2 figure
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