Search Results (39)

We investigated the thermodynamic topology of quantum-corrected AdS-Reissner-Nordström black holes in Kiselev spacetime using non-extensive entropy formulation derived from Loop Quantum Gravity (LQG). Through systematic analysis, we examined how the Tsallis parameter $\lambda$ influences topological charge classification with respect to various equation of state parameters. Our findings revealed a consistent pattern of topological transitions: for $\lambda =0.1$, the system exhibited a single topological charge $(\omega =-1)$ with total charge $W=-1$, as $\lambda$ increased to 0.8, the system transitioned to a configuration with two topological charges $(\omega =+1,-1)$ and total charge $W=0$. When $\lambda =1$, corresponding to the Bekenstein–Hawking entropy limit, the system displayed a single topological charge $(\omega =+1)$ with $W=+1$, signifying thermodynamic stability. The persistence of this pattern across different fluid compositions—from exotic negative pressure environments to radiation—demonstrates the universal nature of quantum gravitational effects on black hole topology. Full article

The first part of this work provides a review of recent research on generalised entropies and their origin, as well as its application to black hole thermodynamics. To start, it is shown that the Hawking temperature and the Bekenstein–Hawking entropy are, respectively, the only possible thermodynamical temperature and entropy of the Schwarzschild black hole. Moreover, it is investigated if the other known generalised entropies, which include Rényi’s entropy, Tsallis entropy, and the four- and five-parameter generalised entropies, could correctly yield the Hawking temperature and the ADM mass. The possibility that generalised entropies could describe hairy black hole thermodynamics is also considered, both for the Reissner–Nordström black hole and for Einstein’s gravity coupled with two scalar fields. Two possibilities are investigated, namely, the case when the ADM mass does not yield the Bekenstein–Hawking entropy, and the case in which the effective mass expressing the energy inside the horizon does not yield the Hawking temperature. For the model with two scalar fields, the radii of the photon sphere and of the black hole shadow are calculated, which gives constraints on the BH parameters. These constraints are seen to be consistent, provided that the black hole is of the Schwarzschild type. Subsequently, the origin of the generalised entropies is investigated, by using their microscopic particle descriptions in the frameworks of a microcanonical ensemble and canonical ensemble, respectively. Finally, the McLaughlin expansion for the generalised entropies is used to derive, in each case, the microscopic interpretation of the generalised entropies, via the canonical and the grand canonical ensembles. Full article

We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann–Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability, we discuss the properties of these entropies and their mutual relations, if they exist. The results are presented in two informative tables that are of strong interest to the gravity and cosmology community in the context of the recently intensively explored horizon entropies for black hole and cosmological models. Gravitational systems admit long-range interactions, which usually lead to a break of the standard additivity rule for thermodynamic systems composed of subsystems in Boltzmann–Gibbs thermodynamics. The features of additivity, extensivity, and composability are listed systematically. A brief discussion on the validity of the notion of equilibrium temperature for nonextensive systems is also presented. Full article

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of $N$ Ising spins coupled to an explicit heat bath of $N$ Einstein oscillators. The simplicity of this system allows the exact entropy to be calculated for the spins and the heat bath for any $N$, with dynamics that is readily altered from reversible to irreversible. We find thermal-equilibrium behavior in the thermodynamic limit, and in systems as small as $N=2$, but both results require microscopic dynamics that is intrinsically irreversible. Full article

Nonextensive statistical mechanics has developed into an important framework for modeling the thermodynamics of complex systems and the information of complex signals. To mark the 80th birthday of the field’s founder, Constantino Tsallis, a review of open problems that can stimulate future research is provided. Over the thirty-year development of NSM, a variety of criticisms have been published ranging from questions about the justification for generalizing the entropy function to the interpretation of the generalizing parameter q. While these criticisms have been addressed in the past and the breadth of applications has demonstrated the utility of the NSM methodologies, this review provides insights into how the field can continue to improve the understanding and application of complex system models. The review starts by grounding q-statistics within scale-shape distributions and then frames a series of open problems for investigation. The open problems include using the degrees of freedom to quantify the difference between entropy and its generalization, clarifying the physical interpretation of the parameter q, improving the definition of the generalized product using multidimensional analysis, defining a generalized Fourier transform applicable to signal processing applications, and re-examining the normalization of nonextensive entropy. This review concludes with a proposal that the shape parameter is a candidate for defining the statistical complexity of a system. Full article

The imminent threat of Mongolian montane forests facing extinction due to climate change emphasizes the pressing need to study these ecosystems for sustainable development. Leveraging multispectral remote sensing data from Landsat 8 OLI TIRS (2013–2021), we apply Tsallis non-extensive thermodynamics to assess spatiotemporal fluctuations in the absorbed solar energy budget (exergy, bound energy, internal energy increment) and organizational parameters (entropy, information increment, q-index) within the mountain taiga–meadow landscape. Using the principal component method, we discern three functional subsystems: evapotranspiration, heat dissipation, and a structural-informational component linked to bioproductivity. The interplay among these subsystems delineates distinct landscape cover states. By categorizing ecosystems (pixels) based on these processes, discrete states and transitional areas (boundaries and potential disturbances) emerge. Examining the temporal dynamics of ecosystems (pixels) within this three-dimensional coordinate space facilitates predictions of future landscape states. Our findings indicate that northern Mongolian montane forests utilize a smaller proportion of received energy for productivity compared to alpine meadows, which results in their heightened vulnerability to climate change. This approach deepens our understanding of ecosystem functioning and landscape dynamics, serving as a basis for evaluating their resilience amid ongoing climate challenges. Full article

Strange hadron transverse momentum spectra are analyzed in symmetric $pp$ and $PbPb$ and asymmetric $pPb$ collision systems for their dependence on rapidity and event charged-particle multiplicity. The thermodynamically consistent Tsallis models with and without flow velocity are used to reproduce the experimental data, extracting the freeze-out parameters to gain insights into the underlying physics of the collision processes by looking into the parameters change with different multiplicities, particle types, and collision geometries. We found that with an increase in the event multiplicity, the average transverse flow velocity, effective, and kinetic freezeout temperatures increase, with heavier strange particle species exhibiting a more significant increase. The value of the non-extensivity parameter decreases with an increase in the multiplicity of the particles. For heavier particles, larger $T_{eff}$ and $T_0$ and smaller q have been observed, confirming the quick thermalization and equilibrium for massive particles. Furthermore, the differences in parameter values for particle species are more significant in $pp$ and $pPb$ collisions than in $PbPb$ collisions. In addition, in symmetric $pp$ and $PbPb$ collisions, parameter values ($q,T_0,{\beta }_T$) show more significant shifts for heavier particles compared to the lighter ones. In contrast, in asymmetric $pPb$ collisions, both heavier and lighter particles display uniform linear progression. Full article

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons in ten groups of centrality of Pb + Pb collisions at $\sqrt{s_{nn}}$ = 2.76 TeV, measured by the ALICE Collaboration, have been analyzed successfully using both thermodynamically consistent and non-consistent Tsallis distribution functions with transverse flow. The collision centrality dependencies of the extracted parameters of two kinds of Tsallis functions with transverse flow have been investigated. The significantly different behavior (growth rates) of ⟨β_T⟩ in regions $⟨N_{part}⟩$ < 71 and $⟨N_{part}⟩$ > 71 with the temperature T₀ becoming constant in region $⟨N_{part}⟩$ > 71 has been observed. This could indicate that $⟨N_{part}⟩$ = 71 ± 5 (corresponding to $⟨d{N}_{ch}/d\eta ⟩$ = 205 ± 15) is a threshold border value of collision centrality for crossover phase transition from the dense hadronic state to the QGP state (or a mixed state of QGP and hadrons) in Pb + Pb collisions at $\sqrt{s_{nn}}$ = 2.76 TeV. This conjecture is supported further by the observed, significantly different correlations between T₀ and $⟨{\beta }_T⟩$ parameters in the corresponding $⟨{\beta }_T⟩$ < 0.44 and $⟨{\beta }_T⟩$ > 0.44 ranges. The strong positive linear correlation between non-extensivity parameter q for pions and kaons, between q for pions and (anti)protons, and between q for kaons and (anti)protons has been obtained. The parameter q for all studied particle species has proven to be strongly anticorrelated with the average transverse flow velocity, ⟨β_T⟩. Quite a large positive linear correlation has been obtained between the q of the studied particle species and temperature parameter T₀. Analysis of q versus $⟨N_{part}⟩$ dependencies for the studied particle species suggests that the highly thermalized and equilibrated QGP is produced in central Pb + Pb collisions at $\sqrt{s_{nn}}$ = 2.76 TeV with $⟨N_{part}⟩$ > 160. Full article

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are successfully analyzed using combined minimum χ² fits with a thermodynamically non-consistent, as well as thermodynamically consistent, Tsallis function with transverse flow. The extracted non-extensivity parameter q decreases systematically for all considered particle species with increasing Pb + Pb collision centrality, suggesting an increase in the degree of system thermalization with an increase in collision centrality. The results for q suggest quite a large degree of thermalization of quark–gluon plasma (QGP) created in central Pb + Pb collisions at $\sqrt{s_{nn} }$= 5.02 TeV with the average number of participant nucleons $⟨N_{part}⟩$ > 160. The obtained significantly different growth rates of transverse flow velocity, $⟨{\beta }_T⟩$, in regions $⟨N_{part}⟩$ < 71 ± 7 and $⟨N_{part}⟩$ > 71 ± 7 with the temperature parameter T₀ remaining constant within uncertainties in region $⟨N_{part}⟩$ > 71 ± 7 probably indicates that $⟨N_{part}⟩$ ≈ 71 ± 7 (corresponding to $⟨d{N}_{ch}/d\eta ⟩$ ≈ 251 ± 20) is a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV. The threshold border value for transverse flow velocity $⟨{\beta }_T⟩$ ≈ 0.46 ± 0.03 (corresponding to $⟨N_{part}⟩$ ≈ 71 ± 7), estimated by us in Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV, agrees well with the corresponding border value $⟨{\beta }_T⟩$ ≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at $\sqrt{s_{nn} }$= 5.44 TeV, and with almost constant $⟨{\beta }_T⟩$ values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, GA, USA) in central Au + Au collisions in the $\sqrt{s_{nn} }$= 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T₀ and $⟨{\beta }_T⟩$ parameters are found to be greatly different in regions $⟨{\beta }_T⟩$ < 0.46 and $⟨{\beta }_T⟩$ > 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at $\sqrt{s_{nn}}$= 5.02 TeV. Full article

In this paper, we provide an account of analytical results related to the Tsallis thermodynamics that have been the subject matter of a lot of studies in the field of high-energy collisions. After reviewing the results for the classical case in the massless limit and for arbitrarily massive classical particles, we compute the quantum thermodynamic variables. For the first time, the analytical formula for the pressure of a Tsallis-like gas of massive bosons has been obtained. The study serves both as a brief review of the knowledge gathered in this area, and as original research that forwards the existing scholarship. The results of the present paper will be important in a plethora of studies in the field of high-energy collisions including the propagation of non-linear waves generated by the traversal of high-energy particles inside the quark-gluon plasma medium showing the features of non-extensivity. Full article

Science and its evolution are based on complex epistemological structures. Two of the pillars of such a construction definitively are enthusiasm and skepticism, both being ingredients without which solid knowledge is hardly achieved and certainly not guaranteed. Our friend and colleague Jean Willy André Cleymans (1944–2021), with his open personality, high and longstanding interest for innovation, and recognized leadership in high-energy physics, constitutes a beautiful example of the former. Recently, Joseph I. Kapusta has generously and laboriously offered an interesting illustration of the latter pillar, in the very same field of physics, concerning the very same theoretical frame, namely, nonextensive statistical mechanics and the nonadditive q-entropies on which it is based. I present here a detailed analysis, point by point, of Kapusta’s 19 May 2021 talk and, placing the discussion in a sensibly wider and updated perspective, I refute his bold conclusion that indices q have no physical foundation. Full article

The transverse momentum $\left(p_T\right)$ spectra of charged particles measured in Au + Au collisions from the beam energy scan (BES) program, Cu + Cu collisions at $\sqrt{s_{NN}}=62.4$, 200 GeV at the RHIC and Pb + Pb, Xe + Xe collisions at the LHC are investigated in the framework of Tsallis thermodynamics. The theory can describe the experimental data well for all the collision systems, energies and centralities investigated. The collision energy and centrality dependence of the Tsallis distribution parameters, i.e., the temperature T and the nonextensive parameter q, for the A + A collisions are also studied and discussed. A novel scaling between the temperature divided by the natural logarithm of collision energy $(T/ln\sqrt{s})$ and the nonextensive parameter q is presented. Full article

The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines focusing on thermodynamical irreversibility of macroscopic physical processes. In the next decade, Boltzmann made the genius connection—further developed by Gibbs—of the entropy with the microscopic world, which led to the formulation of a new and impressively successful physical theory, thereafter named statistical mechanics. The extension to quantum mechanical systems was formalized by von Neumann in 1927, and the connections with the theory of communications and, more widely, with the theory of information were respectively introduced by Shannon in 1948 and Jaynes in 1957. Since then, over fifty new entropic functionals emerged in the scientific and technological literature. The most popular among them are the additive Renyi one introduced in 1961, and the nonadditive one introduced in 1988 as a basis for the generalization of the Boltzmann–Gibbs and related equilibrium and nonequilibrium theories, focusing on natural, artificial and social complex systems. Along such lines, theoretical, experimental, observational and computational efforts, and their connections to nonlinear dynamical systems and the theory of probabilities, are currently under progress. Illustrative applications, in physics and elsewhere, of these recent developments are briefly described in the present synopsis. Full article

This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and shows their connection with the formalism of kappa distributions. By defining the “entropy defect” in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm. Full article