283,712 research outputs found
Relative entropy as a measure of inhomogeneity in general relativity
We introduce the notion of relative volume entropy for two spacetimes with
preferred compact spacelike foliations. This is accomplished by applying the
notion of Kullback-Leibler divergence to the volume elements induced on
spacelike slices. The resulting quantity gives a lower bound on the number of
bits which are necessary to describe one metric given the other. For
illustration, we study some examples, in particular gravitational waves, and
conclude that the relative volume entropy is a suitable device for quantitative
comparison of the inhomogeneity of two spacetimes.Comment: 15 pages, 7 figure
Local Entropy Characterization of Correlated Random Microstructures
A rigorous connection is established between the local porosity entropy
introduced by Boger et al. (Physica A 187, 55 (1992)) and the configurational
entropy of Andraud et al. (Physica A 207, 208 (1994)). These entropies were
introduced as morphological descriptors derived from local volume fluctuations
in arbitrary correlated microstructures occuring in porous media, composites or
other heterogeneous systems. It is found that the entropy lengths at which the
entropies assume an extremum become identical for high enough resolution of the
underlying configurations. Several examples of porous and heterogeneous media
are given which demonstrate the usefulness and importance of this morphological
local entropy concept.Comment: 15 pages. please contact [email protected] and have a look
at http://www.ica1.uni-stuttgart.de/ . To appear in Physica
Phase transition of holographic entanglement entropy in massive gravity
The phase structure of holographic entanglement entropy is studied in massive
gravity for the quantum systems with finite and infinite volumes, which in the
bulk is dual to calculate the minimal surface area for a black hole and black
brane respectively. In the entanglement entropytemperature plane, we find
for both the black hole and black brane there is a Van der Waals-like phase
transition as the case in thermal entropytemperature plane. That is, there
is a first order phase transition for the small charge and a second order phase
transition at the critical charge. For the first order phase transition, the
equal area law is checked and for the second order phase transition, the
critical exponent of the heat capacity is obtained. All the results show that
the phase structure of holographic entanglement entropy is the same as that of
thermal entropy regardless of the volume of the spacetime on the boundary.Comment: 15 pages, many figures, some statments are adde
Cosmological horizon entropy and generalised second law for flat Friedmann Universe
We discuss the generalized second law (GSL) and the constraints imposed by it
for two types of Friedmann universes. The first one is the Friedmann universe
with radiation and a positive cosmological constant, and the second one
consists of non-relativistic matter and a positive cosmological constant. The
time evolution of the event horizon entropy and the entropy of the contents
within the horizon are analyses in an analytical way by obtaining the Hubble
parameter. It is shown that the GSL constraint the temperature of both the
radiation and matter of the Friedmann universe. It is also shown that, even
though the net entropy of the radiation (or matter) is decreasing at
sufficiently large times as the universe expand, it exhibit an increase during
the early times when universe is decelerating. That is the entropy of the
radiation within the comoving volume is decreasing only when the universe has
got an event horizon.Comment: 15 pages, 9 figure
Monopole action and condensation in SU(2) QCD
An effective monopole action for various extended monopoles is derived from
vacuum configurations after abelian projection in the maximally abelian gauge
in QCD. The action appears to be independent of the lattice volume.
Moreover it seems to depend only on the physical lattice spacing of the
renormalized lattice, not on . Entropy dominance over energy of monopole
loops is seen on the renormalized lattice with the spacing . This suggests that monopole condensation
always (for all ) occurs in the infinite-volume limit of lattice QCD.Comment: 15 Pages+7 figures, KANAZAWA 94-1
Maxwell's equal area law and the Hawking-Page phase transition
In this paper we study the phases of a Schwarzschild black hole in the Anti
deSitter background geometry. Exploiting fluid/gravity duality we construct the
Maxwell equal area isotherm T=T* in the temperature-entropy plane, in order to
eliminate negative heat capacity black hole configurations. The construction we
present here is reminiscent of the isobar cut in the pressure-volume plane
which eliminates un-physical part of the Van der Walls curves below the
critical temperature. Our construction also modifies the Hawking-Page phase
transition. Stable black holes are formed at the temperature T > T*, while pure
radiation persists for T< T*. T* turns out to be below the standard
Hawking-Page temperature and there are no unstable black holes as in the usual
scenario. Also, we show that in order to reproduce the correct black hole
entropy S=A/4, one has to write a black hole equation of state, i.e. P=P(V), in
terms of the geometrical volume V=4\pi r^3/3.Comment: 15 pages, 4 Figures. Accepted for publication in Journal of Gravit
The Equation of State for Cool Relativistic Two-Constituent Superfluid Dynamics
The natural relativistic generalisation of Landau's two constituent
superfluid theory can be formulated in terms of a Lagrangian that is given
as a function of the entropy current 4-vector and the gradient
of the superfluid phase scalar. It is shown that in the ``cool"
regime, for which the entropy is attributable just to phonons (not rotons), the
Lagrangian function is given by an expression of the
form where represents the pressure as a function just of
in the (isotropic) cold limit. The entropy current dependent
contribution represents the generalised pressure of the (non-isotropic)
phonon gas, which is obtained as the negative of the corresponding grand
potential energy per unit volume, whose explicit form has a simple algebraic
dependence on the sound or ``phonon" speed that is determined by the cold
pressure function .Comment: 26 pages, RevTeX, no figures, published in Phys. Rev. D. 15 May 199
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