659 research outputs found
Maximum path information and the principle of least action for chaotic system
A path information is defined in connection with the different possible paths
of chaotic system moving in its phase space between two cells. On the basis of
the assumption that the paths are differentiated by their actions, we show that
the maximum path information leads to a path probability distribution as a
function of action from which the well known transition probability of Brownian
motion can be easily derived. An interesting result is that the most probable
paths are just the paths of least action. This suggests that the principle of
least action, in a probabilistic situation, is equivalent to the principle of
maximization of information or uncertainty associated with the probability
distribution.Comment: 12 pages, LaTeX, 1 eps figure, Chaos, Solitons & Fractals (2004), in
pres
Unnormalized nonextensive expectation value and zeroth law of thermodynamics
We show an attempt to establish the zeroth law of thermodynamics within the
framework of nonextensive statistical mechanics based on the classic
normalization and the unnormalized expectation
. The first law of thermodynamics and the
definition of heat and work in this formalism are discussed.Comment: 6 pages, no figure, RevTeX. To appear in Chaos, Solitons & Fractals
(2002
Extensive generalization of statistical mechanics based on incomplete information theory
Statistical mechanics is generalized on the basis of an additive information
theory for incomplete probability distributions. The incomplete normalization
is used to obtain generalized entropy
. The concomitant incomplete statistical
mechanics is applied to some physical systems in order to show the effect of
the incompleteness of information. It is shown that this extensive generalized
statistics can be useful for the correlated electron systems in weak coupling
regime.Comment: 15 pages, 3 eps figures, Te
Correlated electrons and generalized statistics
Several important generalizations of Fermi-Dirac distribution are compared to
numerical and experimental results for correlated electron systems. It is found
that the quantum distributions based on incomplete information hypothesis can
be useful for describing this kind of systems. We show that the additive
incomplete fermion distribution gives very good description of weakly
correlated electrons and that the nonadditive one is suitable to very strong
correlated cases.Comment: 13 pages, RevTex file, 4 ps figures. The European Physical Journal B
(2002), in pres
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