Andrade<i>et al.</i>Reply:

Andrade, José S.; Silva, G. F. T. da; Moreira, André A.; Nobre, Fernando D.; Curado, Evaldo M. F.

doi:10.1103/physrevlett.107.088902

Cited by 17 publications

(10 citation statements)

References 2 publications

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“…During the last two decades, many such phenomena have been successfully approached in the frame of nonextensive statistical mechanics. Predictions, verifications and various applications have been performed in high-energy physics [63][64][65][66][67][68][69][70][71][72], spin-glasses [73], flux of cosmic rays [74], turbulence in pure-electron plasma [75], self-organized criticality in biological evolution [76], cold atoms in optical lattices [77], trapped ions [78], anomalous diffusion [79][80][81][82][83][84], dusty plasmas [85], solar physics [86][87][88], relativistic and nonrelativistic nonlinear quantum mechanics [89][90][91], among many others. If a physical system is constituted by N elements, and these elements are independent (or quasi-independent in some sense), we have that…”

Section: Nonadditive Entropiesmentioning

confidence: 99%

Black hole thermodynamical entropy

2013

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As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy S BG of a (3 + 1) black hole is proportional to its area L 2 (L being a characteristic linear length), and not to its volume L 3 . Similarly it exists the area law, so named because, for a wide class of strongly quantum-entangled d-dimensional systems, S BG is proportional to ln L if d = 1, and to L d−1 if d > 1, instead of being proportional to L d (d ≥ 1). These results violate the extensivity of the thermodynamical entropy of a d-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is not to be identified with the BG additive entropy but with appropriately generalized nonadditive entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.

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Section: Nonadditive Entropiesmentioning

confidence: 99%

Black hole thermodynamical entropy

2013

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“…Thus, at the edge of the profile a continuum description should demand higher orders of approximation. However, this effect becomes negligible in systems where the density profile is not subjected to a strong confinement [24].…”

Section: Arxiv:160209086v1 [Cond-matstat-mech] 29 Feb 2016mentioning

confidence: 99%

General continuum approach for dissipative systems of repulsive particles

et al. 2016

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We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle correlations is incorporated to the overall balance of energy, and a nonlinear diffusion equation is obtained to represent the overdamped dynamics. In particular, when the repulsive interaction potential is a short-ranged power law, our approach reveals a distinctive correspondence between particle-particle energy and the generalized thermostatistics of Tsallis for any nonpositive value of the entropic index q. Our methodology can also be applied to microscopic models of superconducting vortices and complex plasma, where particle-particle correlations are pronounced at low concentrations. The resulting continuum descriptions provide elucidating and useful insights on the microdynamical behavior of these physical systems. The consistency of our approach is demonstrated by comparison with molecular dynamics simulations.

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“…As in Refs. [17,18], periodic boundary conditions are used in the y direction. The equations of motion for each particle i,…”

Section: Molecular Dynamics Simulationsmentioning

confidence: 99%

“…Andrade et al [17,18] and Ribeiro et al [19] have argued that at low temperatures, the vortices in a type II superconductor obey Tsallis statistics (TS). In particular, they claimed that the ground state of interacting vortices in a confining potential corresponds to the maximum of the Tsallis entropy.…”

Section: Molecular Dynamics Simulationsmentioning

confidence: 99%

Vortex distribution in a confining potential

2013

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We study a model of interacting vortices in a type II superconductor. In the weak coupling limit, we constructed a mean-field theory which allows us to accurately calculate the vortex density distribution inside a confining potential. In the strong coupling limit, the correlations between the particles become important and the mean-field theory fails. Contrary to recent suggestions, this does not imply failure of the Boltzmann-Gibbs statistical mechanics, as we clearly demonstrate by comparing the results of molecular dynamics and Monte Carlo simulations.

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Andradeet al.Reply:

Cited by 17 publications

References 2 publications

Black hole thermodynamical entropy

Black hole thermodynamical entropy

General continuum approach for dissipative systems of repulsive particles

Vortex distribution in a confining potential

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