Deformed exponentials and logarithms in generalized thermostatistics

Naudts, Jan

doi:10.1016/s0378-4371(02)01018-x

Cited by 142 publications

(164 citation statements)

References 13 publications

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“…Therefore the appropriate choice of the q index is significant and needs to be examined [34]. It is expected that, for every specific system, better discrimination will be achieved with appropriates ranges of q values [3].…”

Section: Resultsmentioning

confidence: 99%

Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Balasis

Daglis

Papadimitriou

et al. 2011

Entropy

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Over the last couple of decades nonextensive Tsallis entropy has shown remarkable applicability to describe nonequilibrium physical systems with large variability and multifractal structure. Herein, we review recent results from the application of Tsallis statistical mechanics to the detection of dynamical changes related with the occurrence of magnetic storms. We extend our review to describe attempts to approach the dynamics of magnetic storms and solar flares by means of universality through Tsallis statistics. We also include a discussion of possible implications on space weather forecasting efforts arising from the verification of Tsallis entropy in the complex system of the magnetosphere

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Section: Resultsmentioning

confidence: 99%

Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Balasis

Daglis

Papadimitriou

et al. 2011

Entropy

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show abstract

“…This can be easily proved by using the Jensen inequality, ∏ A P i i ≤ ∑ P i A i applied to A i = Q i /P i . The symmetric combination, based on a sum of Bregman type divergences [28][29][30][31],…”

Section: Entropic Distancementioning

confidence: 99%

“…refs. [28][29][30][31]. Furthermore we are interested in a definition which describes a distance that is always shrinking between a dynamically evolving distribution and the one belonging to maximal entropy under a spontaneous dynamics.…”

Section: Introductionmentioning

confidence: 99%

Non-Extensive Entropic Distance Based on Diffusion: Restrictions on Parameters in Entropy Formulae

Bı́ró

Schram

2016

Entropy

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Based on a diffusion-like master equation we propose a formula using the Bregman divergence for measuring entropic distance in terms of different non-extensive entropy expressions. We obtain the non-extensivity parameter range for a universal approach to the stationary distribution by simple diffusive dynamics for the Tsallis and the Kaniadakis entropies, for the Hanel-Thurner generalization, and finally for a recently suggested log-log type entropy formula which belongs to diverging variance in the inverse temperature superstatistics.

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“…The overall damping factor (1+κ∆t) −t/∆t is the deformed exponential [29] occurring in non-extensive thermodynamics [30], and whose links to Gamma-function averages are well known [31].…”

Section: Dissipative and Nondissipative Decoherencementioning

confidence: 99%

Cavity-QED Tests of Representations of Canonical Commutation Relations Employed in Field Quantization

Czachor

Wilczewski

2006

Int J Theor Phys

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Various aspects of dissipative and nondissipative decoherence of Rabi oscillations are discussed in the context of field quantization in alternative representations of CCR. Theory is confronted with experiment, and a possibility of more conclusive tests is analyzed.PACS numbers: 42.50. Pq, 42.50.Xa, 03.70.+k I. CAVITY QED IN DIFFERENT REPRESENTATIONS OF CCRAlthough the notion of entanglement between atomic and electromagnetic degrees of freedom plays a central role in quantum computing architecture based on cavity QED [1,2,3,4,5,6,7,8,9], the very concept of entanglement leads to conceptual difficulties if quantum vacuum comes into play (cf. uniqueness of the vacuum versus violation of the Bell inequality [10], problems with teleportation of quantum fields [11], ambiguous entanglement with vacuum [12,13]). One of the problems is that the electromagnetic field can be quantized in different representations of canonical commutation relations (CCR). As shown in [13] the degree of entanglement is a representation-dependent property, and it is not clear which representations are really physical. The problem is a part of a wider and ongoing discussion on different quantization paradigms [14]. Now, can the available experimental data distinguish between different representations of CCR? The answer is less obvious than one might expect. In this Letter we will try to clarify the status of some data from cavity QED, and then discuss possibilities of more definitive tests.We first analyze at a representation independent level the simple problem of Rabi oscillation of a two-level atom in an ideal cavity (for technicalities we refer to [15] The observed decoherence appears to be entirely of a nondissipative type, but it is not clear why the effect of dissipation is invisible. Perhaps the fact that a photon is with probability 1 absorbed by the atom at times separated by the Rabi period leads to a sort of Zeno effect. This point requires further experimental and theoretical studies, and is beyond the scope of the present paper.Assuming that Rabi oscillations indeed do not reveal observable damping due to energy dissipation we ask to what extent the experiment can distinguish between reducible and irreducible representations of CCR. In physical terms the question can be translated as follows: How many oscillators do we need to model quantum fields? The standard answer is that we need one oscillator per mode. We show that in reducible representations the data only set certain limitations on the number of oscillators, and this number is independent of the number of modes.Finally, we suggest that one should repeat the measurements reported in [18] with better cavities, finer time resolution, and monitor the Rabi oscillation for longer times. The point is that the decay due to experimental imprecisions may mask quantum beats of a completely new type and origin. In principle, the beats can be observed in a form of vacuum collapses and revivals, the effect occurring in reducible N -representations [19]. Observation of the revival...

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Deformed exponentials and logarithms in generalized thermostatistics

Cited by 142 publications

References 13 publications

Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Non-Extensive Entropic Distance Based on Diffusion: Restrictions on Parameters in Entropy Formulae

Cavity-QED Tests of Representations of Canonical Commutation Relations Employed in Field Quantization

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