# Groups, nonadditive entropy and phase transitions

@article{Kalogeropoulos2014GroupsNE, title={Groups, nonadditive entropy and phase transitions}, author={Nikos Kalogeropoulos}, journal={International Journal of Modern Physics B}, year={2014}, volume={28}, pages={1450162} }

We investigate the possibility of discrete groups furnishing a kinematic framework for systems whose thermodynamic behavior may be given by nonadditive entropies. Relying on the well-known result of the growth rate of balls of nilpotent groups, we see that maintaining extensivity of the entropy of a nilpotent group requires using a non-Boltzmann/Gibbs/Shannon (BGS) entropic form. We use the Tsallis entropy as an indicative alternative. Using basic results from hyperbolic and random groups, we…

## 10 Citations

An entropy for groups of intermediate growth

- Physics
- 2017

One of the few accepted dynamical foundations of nonadditive (“nonextensive”) statistical mechanics is that the choice of the appropriate entropy functional describing a system with many degrees of…

Moduli of curve families and (quasi-)conformality of power-law entropies

- Mathematics
- 2015

We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional…

Fractal structure of Yang-mills fields

- Physics
- 2020

The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and…

Ricci Curvature, Isoperimetry and a Non-additive Entropy

- MathematicsEntropy
- 2015

This work presents an isoperimetric interpretation of the non-extensive parameter and comment on further features of the system that can be probed through this tensor.

Fractal Structure and Non-Extensive Statistics

- PhysicsEntropy
- 2018

It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that provided evidence of the connections between those fluctuations and Tsallis statistics.

Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids

- MathematicsEntropy
- 2015

Dvoretzky's theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other and the role that dualities may play in this viewpoint is speculated.

Convexity and the Euclidean metric of space-time

- Mathematics
- 2016

We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness…

The τq-Fourier transform: Covariance and uniqueness

- Mathematics
- 2018

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “τq-Fourier transform”. We comment about the underlying “covariance” on the set of…

Fractal Structures of Yang–Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics

- Physics
- 2020

In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large…

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