2,131 research outputs found
Stability of travelling-wave solutions for reaction-diffusion-convection systems
We are concerned with the asymptotic behaviour of classical solutions of
systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in
RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is
a 'bistable' nonlinearity satisfying conditions which guarantee the existence
of a comparison principle. Suppose that there is a travelling-front solution w
with velocity c, that connects two stable equilibria of f. We show that if U is
bounded, uniformly continuously differentiable and such that w(x) - U(x) is
small when the modulus of x is large, then there exists y in R such that u(.,
t) converges to w(.+y-ct) in the C1 norm at an exponential rate as t tends to
infinity. Our approach extends an idea developed by Roquejoffre, Terman and
Volpert in the convectionless case, where f is independent of u_x.Comment: 23 pages. To appear in Topological Methods in Nonlinear Analysi
Temperature-extended Jarzynski relation: Application to the numerical calculation of the surface tension
We consider a generalization of the Jarzynski relation to the case where the
system interacts with a bath for which the temperature is not kept constant but
can vary during the transformation. We suggest to use this relation as a
replacement to the thermodynamic perturbation method or the Bennett method for
the estimation of the order-order surface tension by Monte Carlo simulations.
To demonstrate the feasibility of the method, we present some numerical data
for the 3D Ising model
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
Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
We study the applications of non-equilibrium relations such as the Jarzynski
equality and fluctuation theorem to spin glasses with gauge symmetry. It is
shown that the exponentiated free-energy difference appearing in the Jarzynski
equality reduces to a simple analytic function written explicitly in terms of
the initial and final temperatures if the temperature satisfies a certain
condition related to gauge symmetry. This result is used to derive a lower
bound on the work done during the non-equilibrium process of temperature
change. We also prove identities relating equilibrium and non-equilibrium
quantities. These identities suggest a method to evaluate equilibrium
quantities from non-equilibrium computations, which may be useful to avoid the
problem of slow relaxation in spin glasses.Comment: 8 pages, 2 figures, submitted to JPS
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
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
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
The thermodynamics of prediction
A system responding to a stochastic driving signal can be interpreted as
computing, by means of its dynamics, an implicit model of the environmental
variables. The system's state retains information about past environmental
fluctuations, and a fraction of this information is predictive of future ones.
The remaining nonpredictive information reflects model complexity that does not
improve predictive power, and thus represents the ineffectiveness of the model.
We expose the fundamental equivalence between this model inefficiency and
thermodynamic inefficiency, measured by dissipation. Our results hold
arbitrarily far from thermodynamic equilibrium and are applicable to a wide
range of systems, including biomolecular machines. They highlight a profound
connection between the effective use of information and efficient thermodynamic
operation: any system constructed to keep memory about its environment and to
operate with maximal energetic efficiency has to be predictive.Comment: 5 pages, 1 figur
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