The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e310" altimg="si6.svg"><mml:mi>q</mml:mi></mml:math>-exponentials do not maximize the Rényi entropy

In the context of Tsallis entropy, we explore the connection between the law of emergence and the thermodynamic laws from a more accurate non-equilibrium perspective. Here, the equilibrium Clausius relation does not conform to the standard energy-momentum conservation. Therefore, an effective gravitational coupling is introduced to rewrite the field equation similar to general relativity, and the corresponding generalized continuity equation is obtained. As a result, thermodynamic laws were modified with the non-equilibrium energy dissipation and entropy production terms, using which we derive the law of emergence. The investigation of the law of emergence and the entropy maximization principle with Tsallis entropy in the non-equilibrium perspective shows that both result in the same constraints as obtained in other gravity theories and the equilibrium context of Tsallis entropy, except for an additional constraint on the Tsallis parameter as a result of extra entropy production. Consequently, the thermodynamic interpretation of the expansion of the universe stays valid even with quantum corrections to the horizon entropy since the correction terms in Tsallis entropy can be treated as the quantum corrections to Bekenstein-Hawking entropy.

mentioning

confidence: 72%

Emergence of cosmic space in Tsallis modified gravity from equilibrium and non-equilibrium thermodynamic perspective

Dheepika,

Mathew

2023

“…In a recent investigation [15], the discussion on the physical temperature is provided based on a detailed study of nonadditive q-entropy maximization. According to a recent investigation on the Rényi entropy [16], the Rényi entropy yields erroneous inferences concerning the optimum distributions of the q-exponential form. Hence, we need more serious investigations for the determination of the parameter q in future works.…”

Section: Derivation Of the Occurrence Scattering Time (Ost)mentioning

confidence: 99%

Influence of Tsallis q-entropy on occurrence scattering time in a nonextensive plasma

Lee,

Ashikawa,

Jung

2023

The essence of Tsallis q-entropy on the occurrence scattering time (OST) process is derived for a nonextensive plasma. The semiclassical eikonal dissection and the nonextensive q-distribution function are used to derive the OST with variables of projectile energy, scattering angle, electron entropic index, ion entropic index, and impact parameter. Our calculations find that the OST advance in a nonextensive plasma decreases with the entropic index. We have seen that the Tsallis q-entropy on the OST advance grows up fast as the scattering angle increases. We also obtained that the nature of Tsallis q-entropy on the OST advance diminishes in forward scattering direction in a nonextensive plasma. Moreover, the authority of the electron q-entropy is found to be greater than the that of ion q-entropy in the cold electron plasma, i.e., when the electron temperature is lower than the ion temperature. However, if the ion temperature is lower than the electron temperature, the authority of the ion q-entropy is more momentous than that of the electron q-entropy.

On the foundations of the maximum entropy principle using Fenchel duality for Shannon and Tsallis entropies

Maréchal,

Navarrete,

Davis

2024

In this work, we address two main objectives. The first one is to provide a rigorous foundation to the maximum entropy principle in statistical physics, by making use of the Fenchel-Rockafellar duality. The second objective is to discuss the well-foundedness of the so-called escort distributions in the context of non-extensive entropy maximization. The duality treatment of maximum entropy confirms the non-rigorous results obtained via the usual variational calculus, however, the use of escort distributions yields undefined behavior when used consistently, and only leads to the desired results when used in an ad-hoc manner.