3,410 research outputs found
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Quantum models of classical mechanics: maximum entropy packets
In a previous paper, a project of constructing quantum models of classical
properties has been started. The present paper concludes the project by turning
to classical mechanics. The quantum states that maximize entropy for given
averages and variances of coordinates and momenta are called ME packets. They
generalize the Gaussian wave packets. A non-trivial extension of the
partition-function method of probability calculus to quantum mechanics is
given. Non-commutativity of quantum variables limits its usefulness. Still, the
general form of the state operators of ME packets is obtained with its help.
The diagonal representation of the operators is found. A general way of
calculating averages that can replace the partition function method is
described. Classical mechanics is reinterpreted as a statistical theory.
Classical trajectories are replaced by classical ME packets. Quantum states
approximate classical ones if the product of the coordinate and momentum
variances is much larger than Planck constant. Thus, ME packets with large
variances follow their classical counterparts better than Gaussian wave
packets.Comment: 26 pages, no figure. Introduction and the section on classical limit
are extended, new references added. Definitive version accepted by Found.
Phy
On the prevalence of non-Gibbsian states in mathematical physics
Gibbs measures are the main object of study in equilibrium statistical
mechanics, and are used in many other contexts, including dynamical systems and
ergodic theory, and spatial statistics. However, in a large number of natural
instances one encounters measures that are not of Gibbsian form. We present
here a number of examples of such non-Gibbsian measures, and discuss some of
the underlying mathematical and physical issues to which they gave rise
Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts model with a Kac-type interaction
We investigate the Gibbs properties of the fuzzy Potts model on the
d-dimensional torus with Kac interaction. We use a variational approach for
profiles inspired by that of Fernandez, den Hollander and Mart{\i}nez for their
study of the Gibbs-non-Gibbs transitions of a dynamical Kac-Ising model on the
torus. As our main result, we show that the mean-field thresholds dividing
Gibbsian from non-Gibbsian behavior are sharp in the fuzzy Kac-Potts model with
class size unequal two. On the way to this result we prove a large deviation
principle for color profiles with diluted total mass densities and use
monotocity arguments.Comment: 20 page
Entropy Analysis of Univariate Biomedical Signals:Review and Comparison of Methods
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