475 research outputs found
Granular Brownian motion with dry friction
The interplay between Coulomb friction and random excitations is studied
experimentally by means of a rotating probe in contact with a stationary
granular gas. The granular material is independently fluidized by a vertical
shaker, acting as a 'heat bath' for the Brownian-like motion of the probe. Two
ball bearings supporting the probe exert nonlinear Coulomb friction upon it.
The experimental velocity distribution of the probe, autocorrelation function,
and power spectra are compared with the predictions of a linear Boltzmann
equation with friction, which is known to simplify in two opposite limits: at
high collision frequency, it is mapped to a Fokker-Planck equation with
nonlinear friction, whereas at low collision frequency, it is described by a
sequence of independent random kicks followed by friction-induced relaxations.
Comparison between theory and experiment in these two limits shows good
agreement. Deviations are observed at very small velocities, where the real
bearings are not well modeled by Coulomb friction.Comment: 7 pages, 6 figure
Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
In this paper we give a complete analysis of the phase transitions in the
mean-field Blume-Emery-Griffiths lattice-spin model with respect to the
canonical ensemble, showing both a second-order, continuous phase transition
and a first-order, discontinuous phase transition for appropriate values of the
thermodynamic parameters that define the model. These phase transitions are
analyzed both in terms of the empirical measure and the spin per site by
studying bifurcation phenomena of the corresponding sets of canonical
equilibrium macrostates, which are defined via large deviation principles.
Analogous phase transitions with respect to the microcanonical ensemble are
also studied via a combination of rigorous analysis and numerical calculations.
Finally, probabilistic limit theorems for appropriately scaled values of the
total spin are proved with respect to the canonical ensemble. These limit
theorems include both central-limit-type theorems when the thermodynamic
parameters are not equal to critical values and non-central-limit-type theorems
when these parameters equal critical values.Comment: 33 pages, revtex
Specific heat and entropy of -body nonextensive systems
We have studied finite -body -dimensional nonextensive ideal gases and
harmonic oscillators, by using the maximum-entropy methods with the - and
normal averages (: the entropic index). The validity range, specific heat
and Tsallis entropy obtained by the two average methods are compared. Validity
ranges of the - and normal averages are ,
respectively, where , and
() for ideal gases (harmonic oscillators). The energy and
specific heat in the - and normal averages coincide with those in the
Boltzmann-Gibbs statistics, % independently of , although this coincidence
does not hold for the fluctuation of energy. The Tsallis entropy for obtained by the -average is quite different from that derived by the
normal average, despite a fairly good agreement of the two results for . It has been pointed out that first-principles approaches previously
proposed in the superstatistics yield -body entropy () which is in contrast with the Tsallis entropy.Comment: 27 pages, 8 figures: augmented the tex
Generalized canonical ensembles and ensemble equivalence
This paper is a companion article to our previous paper (J. Stat. Phys. 119,
1283 (2005), cond-mat/0408681), which introduced a generalized canonical
ensemble obtained by multiplying the usual Boltzmann weight factor of the canonical ensemble with an exponential factor involving a continuous
function of the Hamiltonian . We provide here a simplified introduction
to our previous work, focusing now on a number of physical rather than
mathematical aspects of the generalized canonical ensemble. The main result
discussed is that, for suitable choices of , the generalized canonical
ensemble reproduces, in the thermodynamic limit, all the microcanonical
equilibrium properties of the many-body system represented by even if this
system has a nonconcave microcanonical entropy function. This is something that
in general the standard () canonical ensemble cannot achieve. Thus a
virtue of the generalized canonical ensemble is that it can be made equivalent
to the microcanonical ensemble in cases where the canonical ensemble cannot.
The case of quadratic -functions is discussed in detail; it leads to the
so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title
changed, references updated, new paragraph added, minor differences with
published versio
Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects
The temperature-dependent uniform magnetic susceptibility of interacting
electrons in one dimension is calculated using several methods. At low
temperature, the renormalization group reaveals that the Luttinger liquid spin
susceptibility approaches zero temperature with an infinite slope
in striking contrast with the Fermi liquid result and with the behavior of the
compressibility in the absence of umklapp scattering. This effect comes from
the leading marginally irrelevant operator, in analogy with the Heisenberg spin
1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher
temperature reveal that non-logarithmic terms are important in that regime.
These contributions are evaluated from an effective interaction that includes
the same set of diagrams as those that give the leading logarithmic terms in
the renormalization group approach. Comments on the third law of thermodynamics
as well as reasons for the failure of approaches that work in higher dimensions
are given.Comment: 21 pages, latex including 5 eps figure
Information and flux in a feedback controlled Brownian ratchet
We study a feedback control version of the flashing Brownian ratchet, in
which the application of the flashing potential depends on the state of the
particles to be controlled. Taking the view that the ratchet acts as a
Maxwell's demon, we study the relationship that exists between the performance
of the demon as a rectifier of random motion and the amount of information
gathered by the demon through measurements. In the context of a simple
measurement model, we derive analytic expressions for the flux induced by the
feedback ratchet when acting on one particle and a few particles, and compare
these results with those obtained with its open-loop version, which operates
without information. Our main finding is that the flux in the feedback case has
an upper bound proportional to the square-root of the information. Our results
provide a quantitative analysis of the value of information in feedback
ratchets, as well as an effective description of imperfect or noisy feedback
ratchets that are relevant for experimental applications.Comment: LaTeX, 13 pages, 2 figure
Possible thermodynamic structure underlying the laws of Zipf and Benford
We show that the laws of Zipf and Benford, obeyed by scores of numerical data
generated by many and diverse kinds of natural phenomena and human activity are
related to the focal expression of a generalized thermodynamic structure. This
structure is obtained from a deformed type of statistical mechanics that arises
when configurational phase space is incompletely visited in a severe way.
Specifically, the restriction is that the accessible fraction of this space has
fractal properties. The focal expression is an (incomplete) Legendre transform
between two entropy (or Massieu) potentials that when particularized to first
digits leads to a previously existing generalization of Benford's law. The
inverse functional of this expression leads to Zipf's law; but it naturally
includes the bends or tails observed in real data for small and large rank.
Remarkably, we find that the entire problem is analogous to the transition to
chaos via intermittency exhibited by low-dimensional nonlinear maps. Our
results also explain the generic form of the degree distribution of scale-free
networks.Comment: To be published in European Physical Journal
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