1,960 research outputs found
Measuring thermodynamic length
Thermodynamic length is a metric distance between equilibrium thermodynamic
states. Among other interesting properties, this metric asymptotically bounds
the dissipation induced by a finite time transformation of a thermodynamic
system. It is also connected to the Jensen-Shannon divergence, Fisher
information and Rao's entropy differential metric. Therefore, thermodynamic
length is of central interest in understanding matter out-of-equilibrium. In
this paper, we will consider how to define thermodynamic length for a small
system described by equilibrium statistical mechanics and how to measure
thermodynamic length within a computer simulation. Surprisingly, Bennett's
classic acceptance ratio method for measuring free energy differences also
measures thermodynamic length.Comment: 4 pages; Typos correcte
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
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
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
Nonequilibrium work on spin glasses in longitudinal and transverse fields
We derive a number of exact relations between equilibrium and nonequilibrium
quantities for spin glasses in external fields using the Jarzynski equality and
gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is
established for the work done on the system in nonequilibrium processes, and
identities are proven to relate equilibrium and nonequilibrium quantities. In
the case of uniform transverse fields, identities are proven between physical
quantities and exponentiated work done to the system at different parts of the
phase diagram with the context of quantum annealing in mind. Additional
relations are given, which relate the exponentiated work in quantum and
simulated (classical) annealing. It is also suggested that the Jarzynski
equality may serve as a guide to develop a method to perform quantum annealing
under non-adiabatic conditions.Comment: 17 pages, 5 figures, submitted to JPS
Microscopic analysis of the microscopic reversibility in quantum systems
We investigate the robustness of the microscopic reversibility in open
quantum systems which is discussed by Monnai [arXiv:1106.1982 (2011)]. We
derive an exact relation between the forward transition probability and the
reversed transition probability in the case of a general measurement basis. We
show that the microscopic reversibility acquires some corrections in general
and discuss the physical meaning of the corrections. Under certain processes,
some of the correction terms vanish and we numerically confirmed that the
remaining correction term becomes negligible; the microscopic reversibility
almost holds even when the local system cannot be regarded as macroscopic.Comment: 12 pages, 10 figure
Thermodynamic metrics and optimal paths
A fundamental problem in modern thermodynamics is how a molecular-scale
machine performs useful work, while operating away from thermal equilibrium
without excessive dissipation. To this end, we derive a friction tensor that
induces a Riemannian manifold on the space of thermodynamic states. Within the
linear-response regime, this metric structure controls the dissipation of
finite-time transformations, and bestows optimal protocols with many useful
properties. We discuss the connection to the existing thermodynamic length
formalism, and demonstrate the utility of this metric by solving for optimal
control parameter protocols in a simple nonequilibrium model.Comment: 5 page
A Quantum Analogue of the Jarzynski Equality
A quantum analogue of the Jarzynski equality is constructed. This equality
connects an ensemble average of exponentiated work with the Helmholtz
free-energy difference in a nonequilibrium switching process subject to a
thermal heat bath. To confirm its validity in a practical situation, we also
investigate an open quantum system that is a spin 1/2 system with a scanning
magnetic field interacting with a thermal heat bath. As a result, we find that
the quantum analogue functions well.Comment: 7 pages, 1 figure; to appear in J. Phys. Soc. Jpn. 69 (2000
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