67 research outputs found
Equilibrium distributions in entropy driven balanced processes
For entropy driven balanced processes we obtain final states with Poisson,
Bernoulli, negative binomial and P\'olya distributions. We apply this both for
complex networks and particle production. For random networks we follow the
evolution of the degree distribution, , in a system where a node can
activate fixed connections from possible partnerships among all nodes.
The total number of connections, , is also fixed. For particle physics
problems is the probability of having particles (or other quanta)
distributed among states (phase space cells) while altogether a fixed
number of particles reside on states.Comment: 12 pages no figure
Entropic Distance for Nonlinear Master Equation
More and more works deal with statistical systems far from equilibrium,
dominated by unidirectional stochastic processes augmented by rare resets. We
analyze the construction of the entropic distance measure appropriate for such
dynamics. We demonstrate that a power-like nonlinearity in the state
probability in the master equation naturally leads to the Tsallis
(Havrda-Charv\'at, Acz\'el-Dar\'oczy) q-entropy formula in the context of
seeking for the maximal entropy state at stationarity. A few possible
applications of a certain simple and linear master equation to phenomena
studied in statistical physics are listed at the end.Comment: Talk given by T.S.Bir\'o at BGL 2017, Gy\"ongy\"os, Hungar
Stochastic Resonance in 3D Ising Ferromagnets
Finite 3D Ising ferromagnets are studied in periodic magnetic fields both by
computer simulations and mean-field theoretical approaches. The phenomenon of
stochastic resonance is revealed. The characteristic peak obtained for the
correlation function between the external oscillating magnetic field and
magnetization versus the temperature of the system, is studied for various
external fields and lattice sizes. Excellent agreement between simulation and
theoretical results are obtained.Comment: 12 pages, 6 Postscript figures upon request, typset in Late
Response in kinetic Ising model to oscillating magnetic fields
Ising models obeying Glauber dynamics in a temporally oscillating magnetic
field are analyzed. In the context of stochastic resonance, the response in the
magnetization is calculated by means of both a mean-field theory with
linear-response approximation, and the time-dependent Ginzburg-Landau equation.
Analytic results for the temperature and frequency dependent response,
including the resonance temperature, compare favorably with simulation data.Comment: RevTex, 6 pages, two-column, 2 figure
Gintropy: Gini index based generalization of Entropy
Entropy is being used in physics, mathematics, informatics and in related
areas to describe equilibration, dissipation, maximal probability states and
optimal compression of information. The Gini index on the other hand is an
established measure for social and economical inequalities in a society. In
this paper we explore the mathematical similarities and connections in these
two quantities and introduce a new measure that is capable to connect these two
at an interesting analogy level. This supports the idea that a generalization
of the Gibbs--Boltzmann--Shannon entropy, based on a transformation of the
Lorenz curve, can properly serve in quantifying different aspects of complexity
in socio- and econo-physics.Comment: 13 pages, 3 Figure
Hierarchical Settlement Networks
A network representation is introduced for visualizing hierarchical region structures on
various spatial scales. The method is based on a spring-block model approach borrowed
from physics; it was previously used successfully to detect regions in any geographical
space. Transylvania, USA and Hungary are used to demonstrate the network construction
metho
Winning strategies in congested traffic
One-directional traffic on two-lanes is modeled in the framework of a
spring-block type model. A fraction of the cars are allowed to change
lanes, following simple dynamical rules, while the other cars keep their
initial lane. The advance of cars, starting from equivalent positions and
following the two driving strategies is studied and compared. As a function of
the parameter the winning probability and the average gain in the
advancement for the lane-changing strategy is computed. An interesting
phase-transition like behavior is revealed and conclusions are drawn regarding
the conditions when the lane changing strategy is the better option for the
drivers.Comment: 5 pages, 5 figure
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