19,546 research outputs found
The entropy in finite -unit nonextensive systems: the ordinary average and -average
We have discussed the Tsallis entropy in finite -unit nonextensive
systems, by using the multivariate -Gaussian probability distribution
functions (PDFs) derived by the maximum entropy methods with the normal average
and the -average (: the entropic index). The Tsallis entropy obtained by
the -average has an exponential dependence: for large (). In
contrast, the Tsallis entropy obtained by the normal average is given by
for large (.
dependences of the Tsallis entropy obtained by the - and normal averages are
generally quite different, although the both results are in fairly good
agreement for . The validity of the factorization
approximation to PDFs which has been commonly adopted in the literature, has
been examined. We have calculated correlations defined by for where , and
the bracket stands for the normal and -averages. The
first-order correlation () expresses the intrinsic correlation and
higher-order correlations with include nonextensivity-induced
correlation, whose physical origin is elucidated in the superstatistics.Comment: 23 pages, 5 figures: the final version accepted in J. Math. Phy
Recombination kinetics of a dense electron-hole plasma in strontium titanate
We investigated the nanosecond-scale time decay of the blue-green light
emitted by nominally pure SrTiO following the absorption of an intense
picosecond laser pulse generating a high density of electron-hole pairs. Two
independent components are identified in the fluorescence signal that show a
different dynamics with varying excitation intensity, and which can be
respectively modeled as a bimolecular and unimolecolar process. An
interpretation of the observed recombination kinetics in terms of interacting
electron and hole polarons is proposed
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
Violation of Bell-like Inequality for spin-energy entanglement in neutron polarimetry
Violation of a Bell-like inequality for a spin-energy entangled neutron state
has been confirmed in a polarimetric experiment. The proposed inequality, in
Clauser-Horne-Shimony-Holt (CHSH) formalism, relies on correlations between the
spin and energy degree of freedom in a single-neutron system. The entangled
states are generated utilizing a suitable combination of two radio-frequency
fields in a neutron polarimeter setup. The correlation function S is determined
to be 2.333+/-0.005, which violates the Bell-like CHSH inequality by more than
66 standard deviations.Comment: 4 pages 2 figure
Quasi Markovian behavior in mixing maps
We consider the time dependent probability distribution of a coarse grained
observable Y whose evolution is governed by a discrete time map. If the map is
mixing, the time dependent one-step transition probabilities converge in the
long time limit to yield an ergodic stochastic matrix. The stationary
distribution of this matrix is identical to the asymptotic distribution of Y
under the exact dynamics. The nth time iterate of the baker map is explicitly
computed and used to compare the time evolution of the occupation probabilities
with those of the approximating Markov chain. The convergence is found to be at
least exponentially fast for all rectangular partitions with Lebesgue measure.
In particular, uniform rectangles form a Markov partition for which we find
exact agreement.Comment: 16 pages, 1 figure, uses elsart.sty, to be published in Physica D
Special Issue on Predictability: Quantifying Uncertainty in Models of Complex
Phenomen
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