30,847 research outputs found
The Thermal Abundance of Semi-Relativistic Relics
Approximate analytical solutions of the Boltzmann equation for particles that
are either extremely relativistic or non-relativistic when they decouple from
the thermal bath are well established. However, no analytical formula for the
relic density of particles that are semi-relativistic at decoupling is yet
known. We propose a new ansatz for the thermal average of the annihilation
cross sections for such particles, and find a semi-analytical treatment for
calculating their relic densities. As examples, we consider Majorana- and
Dirac-type neutrinos. We show that such semi-relativistic relics cannot be good
cold Dark Matter candidates. However, late decays of meta-stable
semi-relativistic relics might have released a large amount of entropy, thereby
diluting the density of other, unwanted relics.Comment: 22 pages, 5 figures. Comments and references adde
Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models
The cluster variation method (CVM) is a hierarchy of approximate variational
techniques for discrete (Ising--like) models in equilibrium statistical
mechanics, improving on the mean--field approximation and the Bethe--Peierls
approximation, which can be regarded as the lowest level of the CVM. In recent
years it has been applied both in statistical physics and to inference and
optimization problems formulated in terms of probabilistic graphical models.
The foundations of the CVM are briefly reviewed, and the relations with
similar techniques are discussed. The main properties of the method are
considered, with emphasis on its exactness for particular models and on its
asymptotic properties.
The problem of the minimization of the variational free energy, which arises
in the CVM, is also addressed, and recent results about both provably
convergent and message-passing algorithms are discussed.Comment: 36 pages, 17 figure
Exact Probability Distribution versus Entropy
The problem addressed concerns the determination of the average number of
successive attempts of guessing a word of a certain length consisting of
letters with given probabilities of occurrence. Both first- and second-order
approximations to a natural language are considered. The guessing strategy used
is guessing words in decreasing order of probability. When word and alphabet
sizes are large, approximations are necessary in order to estimate the number
of guesses. Several kinds of approximations are discussed demonstrating
moderate requirements concerning both memory and CPU time. When considering
realistic sizes of alphabets and words (100) the number of guesses can be
estimated within minutes with reasonable accuracy (a few percent). For many
probability distributions the density of the logarithm of probability products
is close to a normal distribution. For those cases it is possible to derive an
analytical expression for the average number of guesses. The proportion of
guesses needed on average compared to the total number decreases almost
exponentially with the word length. The leading term in an asymptotic expansion
can be used to estimate the number of guesses for large word lengths.
Comparisons with analytical lower bounds and entropy expressions are also
provided
Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres
The residual multiparticle entropy (RMPE) of a fluid is defined as the
difference, , between the excess entropy per particle (relative to an
ideal gas with the same temperature and density), , and the
pair-correlation contribution, . Thus, the RMPE represents the net
contribution to due to spatial correlations involving three,
four, or more particles. A heuristic `ordering' criterion identifies the
vanishing of the RMPE as an underlying signature of an impending structural or
thermodynamic transition of the system from a less ordered to a more spatially
organized condition (freezing is a typical example). Regardless of this, the
knowledge of the RMPE is important to assess the impact of non-pair
multiparticle correlations on the entropy of the fluid. Recently, an accurate
and simple proposal for the thermodynamic and structural properties of a
hard-sphere fluid in fractional dimension has been proposed [Santos,
A.; L\'opez de Haro, M. \emph{Phys. Rev. E} \textbf{2016}, \emph{93}, 062126].
The aim of this work is to use this approach to evaluate the RMPE as a function
of both and the packing fraction . It is observed that, for any given
dimensionality , the RMPE takes negative values for small densities, reaches
a negative minimum at a packing fraction
, and then rapidly increases, becoming positive beyond a
certain packing fraction . Interestingly, while both
and monotonically decrease as dimensionality
increases, the value of exhibits a nonmonotonic
behavior, reaching an absolute minimum at a fractional dimensionality . A plot of the scaled RMPE shows a
quasiuniversal behavior in the region .Comment: 10 pages, 3 figures; v2: minor change
A simple ansatz to describe thermodynamic quantities of peptides and proteins at low temperatures
We describe a simple ansatz to approximate the low temperature behavior of
proteins and peptides by a mean-field-like model which is analytically
solvable. For a small peptide some thermodynamic quantities are calculated and
compared with numerical results of an all-atoms simulation. Our approach can be
used to determine the weights for a multicanonical simulation of the molecule
under consideration.Comment: 11 pages, Latex, 4 Postscript figures, to appear in Int. J. Mod.
Phys. C (1997
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