2,612 research outputs found
On the Quantum Jarzynski Identity
In this note, we will discuss how to compactly express and prove the
Jarzynski identity for an open quantum system with dissipative dynamics. We
will avoid explicitly measuring the work directly, which is tantamount to
continuously monitoring the system, and instead measure the heat flow from the
environment. We represent the measurement of heat flow with Hermitian map
superoperators that act on the system density matrix. Hermitian maps provide a
convenient and compact representation of sequential measurement and correlation
functions.Comment: 4 page
Water-resource records of Brevard County, Florida
The U. S. Geological Survey made a comprehensive
investigation of the water resources of Brevard County
from 1954 to 1958. The purposes of this investigation were:
(1) to determine the occurrence and chemical quality of
water in the streams and lakes, (2) to determine the location
and the thickness of aquifers, and (3) to determine the
occurrence and chemical quality of the ground water. During
the period from 1933 to 1954, water records were collected
from a few stream-gaging stations and a few observation
wells. The purpose of this report is to present basic data
collected during these investigations. (Document has 188 pages.
Quantum Operation Time Reversal
The dynamics of an open quantum system can be described by a quantum
operation, a linear, complete positive map of operators. Here, I exhibit a
compact expression for the time reversal of a quantum operation, which is
closely analogous to the time reversal of a classical Markov transition matrix.
Since open quantum dynamics are stochastic, and not, in general, deterministic,
the time reversal is not, in general, an inversion of the dynamics. Rather, the
system relaxes towards equilibrium in both the forward and reverse time
directions. The probability of a quantum trajectory and the conjugate, time
reversed trajectory are related by the heat exchanged with the environment.Comment: 4 page
Microscopic reversibility of quantum open systems
The transition probability for time-dependent unitary evolution is invariant
under the reversal of protocols just as in the classical Liouvillian dynamics.
In this article, we generalize the expression of microscopic reversibility to
externally perturbed large quantum open systems. The time-dependent external
perturbation acts on the subsystem during a transient duration, and
subsequently the perturbation is switched off so that the total system would
thermalize. We concern with the transition probability for the subsystem
between the initial and final eigenstates of the subsystem. In the course of
time evolution, the energy is irreversibly exchanged between the subsystem and
reservoir. The time reversed probability is given by the reversal of the
protocol and the initial ensemble. Microscopic reversibility equates the time
forward and reversed probabilities, and therefore appears as a thermodynamic
symmetry for open quantum systems.Comment: numerical demonstration is correcte
Near-equilibrium measurements of nonequilibrium free energy
A central endeavor of thermodynamics is the measurement of free energy
changes. Regrettably, although we can measure the free energy of a system in
thermodynamic equilibrium, typically all we can say about the free energy of a
non-equilibrium ensemble is that it is larger than that of the same system at
equilibrium. Herein, we derive a formally exact expression for the probability
distribution of a driven system, which involves path ensemble averages of the
work over trajectories of the time-reversed system. From this we find a simple
near-equilibrium approximation for the free energy in terms of an excess mean
time-reversed work, which can be experimentally measured on real systems. With
analysis and computer simulation, we demonstrate the accuracy of our
approximations for several simple models.Comment: 5 pages, 3 figure
Posterior probability and fluctuation theorem in stochastic processes
A generalization of fluctuation theorems in stochastic processes is proposed.
The new theorem is written in terms of posterior probabilities, which are
introduced via the Bayes theorem. In usual fluctuation theorems, a forward path
and its time reversal play an important role, so that a microscopically
reversible condition is essential. In contrast, the microscopically reversible
condition is not necessary in the new theorem. It is shown that the new theorem
adequately recovers various theorems and relations previously known, such as
the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the
Hatano-Sasa relation, when adequate assumptions are employed.Comment: 4 page
Fluctuation Theorem in Rachet System
Fluctuation Theorem(FT) has been studied as far from equilibrium theorem,
which relates the symmetry of entropy production. To investigate the
application of this theorem, especially to biological physics, we consider the
FT for tilted rachet system. Under, natural assumption, FT for steady state is
derived.Comment: 6 pages, 2 figure
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
Transient fluctuation theorem in closed quantum systems
Our point of departure are the unitary dynamics of closed quantum systems as
generated from the Schr\"odinger equation. We focus on a class of quantum
models that typically exhibit roughly exponential relaxation of some observable
within this framework. Furthermore, we focus on pure state evolutions. An
entropy in accord with Jaynes principle is defined on the basis of the quantum
expectation value of the above observable. It is demonstrated that the
resulting deterministic entropy dynamics are in a sense in accord with a
transient fluctuation theorem. Moreover, we demonstrate that the dynamics of
the expectation value are describable in terms of an Ornstein-Uhlenbeck
process. These findings are demonstrated numerically and supported by
analytical considerations based on quantum typicality.Comment: 5 pages, 6 figure
The length of time's arrow
An unresolved problem in physics is how the thermodynamic arrow of time
arises from an underlying time reversible dynamics. We contribute to this issue
by developing a measure of time-symmetry breaking, and by using the work
fluctuation relations, we determine the time asymmetry of recent single
molecule RNA unfolding experiments. We define time asymmetry as the
Jensen-Shannon divergence between trajectory probability distributions of an
experiment and its time-reversed conjugate. Among other interesting properties,
the length of time's arrow bounds the average dissipation and determines the
difficulty of accurately estimating free energy differences in nonequilibrium
experiments
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