2,733 research outputs found
Gravitational entropy of black holes and wormholes
Pure thermodynamical considerations to describe the entropic evolution of the
universe seem to violate the Second Law of Thermodynamics. This suggests that
the gravitational field itself has entropy. In this paper we expand recent work
done by Rudjord, Gr{\O}n and Sigbj{\O}rn where they suggested a method to
calculate the gravitational entropy in black holes based on the so-called `Weyl
curvature conjecture'. We study the formulation of an estimator for the
gravitational entropy of Reissner-Nordstr\"om, Kerr, Kerr-Newman black holes,
and a simple case of wormhole. We calculate in each case the entropy for both
horizons and the interior entropy density. Then, we analyse whether the
functions obtained have the expected behaviour for an appropriate description
of the gravitational entropy density.Comment: 11 pages, 11 figures, accepted for publication in International
Journal of Theoretical Physic
Expansion potentials for exact far-from-equilibrium spreading of particles and energy
The rates at which energy and particle densities move to equalize arbitrarily
large temperature and chemical potential differences in an isolated quantum
system have an emergent thermodynamical description whenever energy or particle
current commutes with the Hamiltonian. Concrete examples include the energy
current in the 1D spinless fermion model with nearest-neighbor interactions
(XXZ spin chain), energy current in Lorentz-invariant theories or particle
current in interacting Bose gases in arbitrary dimension. Even far from
equilibrium, these rates are controlled by state functions, which we call
``expansion potentials'', expressed as integrals of equilibrium Drude weights.
This relation between nonequilibrium quantities and linear response implies
non-equilibrium Maxwell relations for the Drude weights. We verify our results
via DMRG calculations for the XXZ chain.Comment: v2: to appear in PR
Modelling the kinetics of transesterification reaction of sunflower oil with ethanol in microreactors
Transesterification reaction of vegetable oil with ethanol leads to ethyl esters, used to date for applications principally in food and cosmetic industry. To open the application field to biofuels (to substitute current fuels resulting from fossil resources), the process efficiency has to be developed to be economically profitable. In this work, the sunflower oil ethanolysis was performed in a micro-scaled continuous device, inducing better control for heat and mass transfer in comparison with batch processes. Moreover, this device ensures kinetic data acquisition at the first seconds of the reaction, which was not feasible in a conventional batch process. These data were used to model occurring phenomena and to determine kinetic constants and mass transfer coefficients. A single set of these parameters is able to represent the evolution of the reaction media composition function of time for five ethanol to oil molar ratios (6.0, 9.0, 16.2, 22.7 and 45.4). The model was validated in reaction and diffusion mode. Finally, it was subsequently used to simulate reactions with other operational conditions and to propose other process implementation
Distributed stochastic optimization via matrix exponential learning
In this paper, we investigate a distributed learning scheme for a broad class
of stochastic optimization problems and games that arise in signal processing
and wireless communications. The proposed algorithm relies on the method of
matrix exponential learning (MXL) and only requires locally computable gradient
observations that are possibly imperfect and/or obsolete. To analyze it, we
introduce the notion of a stable Nash equilibrium and we show that the
algorithm is globally convergent to such equilibria - or locally convergent
when an equilibrium is only locally stable. We also derive an explicit linear
bound for the algorithm's convergence speed, which remains valid under
measurement errors and uncertainty of arbitrarily high variance. To validate
our theoretical analysis, we test the algorithm in realistic
multi-carrier/multiple-antenna wireless scenarios where several users seek to
maximize their energy efficiency. Our results show that learning allows users
to attain a net increase between 100% and 500% in energy efficiency, even under
very high uncertainty.Comment: 31 pages, 3 figure
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