96,210 research outputs found
On the way towards a generalized entropy maximization procedure
We propose a generalized entropy maximization procedure, which takes into
account the generalized averaging procedures and information gain definitions
underlying the generalized entropies. This novel generalized procedure is then
applied to Renyi and Tsallis entropies. The generalized entropy maximization
procedure for Renyi entropies results in the exponential stationary
distribution asymptotically for q is between [0,1] in contrast to the
stationary distribution of the inverse power law obtained through the ordinary
entropy maximization procedure. Another result of the generalized entropy
maximization procedure is that one can naturally obtain all the possible
stationary distributions associated with the Tsallis entropies by employing
either ordinary or q-generalized Fourier transforms in the averaging procedure.Comment: 12 pages, no figure
Cosmological evolution of the gravitational entropy of the large-scale structure
We consider the entropy associated with the large-scale structure of the
Universe in the linear regime, where the Universe can be described by a
perturbed Friedmann-Lema\^itre spacetime. In particular, we compare two
different definitions proposed in the literature for the entropy using a
spatial averaging prescription. For one definition, the entropy of the
large-scale structure for a given comoving volume always grows with time, both
for a CDM and a CDM model. In particular, while it diverges for a CDM
model, it saturates to a constant value in the presence of a cosmological
constant. The use of a light-cone averaging prescription in the context of the
evaluation of the entropy is also discussed.Comment: 10 pages, 4 figures. Presentation improved, typos corrected, previous
subsection III.B merged with subsection II.C, comments, clarifications and a
reference added. Version accepted for publication in GR
Euclidean Path Integral, D0-Branes and Schwarzschild Black Holes in Matrix Theory
The partition function in Matrix theory is constructed by Euclidean path
integral method. The D0-branes, which move around in the finite region with a
typical size of Schwarzschild radius, are chosen as the background. The mass
and entropy of the system obtained from the partition function contain the
parameters of the background. After averaging the mass and entropy over the
parameters, we find that they match the properties of 11D Schwarzschild black
holes. The period \b of Euclidean time can be identified with the reciprocal
of the boosted Hawking temperature. The entropy is shown to be proportional
to the number of Matrix theory partons, which is a consequence of the
D0-brane background.Comment: 15 pages, Late
Chaos for Liouville probability densities
Using the method of symbolic dynamics, we show that a large class of
classical chaotic maps exhibit exponential hypersensitivity to perturbation,
i.e., a rapid increase with time of the information needed to describe the
perturbed time evolution of the Liouville density, the information attaining
values that are exponentially larger than the entropy increase that results
from averaging over the perturbation. The exponential rate of growth of the
ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the
map. These findings generalize and extend results obtained for the baker's map
[R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.
A derivation of a microscopic entropy and time irreversibility from the discreteness of time
All of the basic microsopic physical laws are time reversible. In contrast,
the second law of thermodynamics, which is a macroscopic physical
representation of the world, is able to describe irreversible processes in an
isolated system through the change of entropy S larger than 0. It is the
attempt of the present manuscript to bridge the microscopic physical world with
its macrosocpic one with an alternative approach than the statistical mechanics
theory of Gibbs and Boltzmann. It is proposed that time is discrete with
constant step size. Its consequence is the presence of time irreversibility at
the microscopic level if the present force is of complex nature (i.e. not
const). In order to compare this discrete time irreversible mechamics (for
simplicity a classical, single particle in a one dimensional space is selected)
with its classical Newton analog, time reversibility is reintroduced by scaling
the time steps for any given time step n by the variable sn leading to the
Nose-Hoover Lagrangian. The corresponding Nose-Hoover Hamiltonian comprises a
term Ndf *kB*T*ln(sn) (with kB the Boltzmann constant, T the temperature, and
Ndf the number of degrees of freedom) which is defined as the microscopic
entropy Sn at time point n multiplied by T. Upon ensemble averaging this
microscopic entropy Sn in equilibrium for a system which does not have fast
changing forces approximates its macroscopic counterpart known from
thermodynamics. The presented derivation with the resulting analogy between the
ensemble averaged microscopic entropy and its thermodynamic analog suggests
that the original description of the entropy by Boltzmann and Gibbs is just an
ensemble averaging of the time scaling variable sn which is in equilibrium
close to 1, but that the entropy term itself has its root not in statistical
mechanics but rather in the discreteness of time
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