Black Hole Thermodynamics via Tsallis Statistical Mechanics
arXiv:2502.02522 · doi:10.1140/epjc/s10052-025-14239-1
Abstract
An investigation of black hole thermodynamics based on Tsallis statistical mechanics is explored through the study of the thermodynamics of a gas system located near the horizon of a black hole. In spite of the difficulty in exploring black hole thermodynamics through statistical mechanics, the entropy of the nearby gas system is found to be proportional to the black hole's horizon area using Gibbs-Boltzmann statistical mechanics. This allows us to study black hole thermodynamics by using statistical mechanics through the thermodynamic behaviors of the gas system. Since the entropy of the black hole is proportional to the horizon area, it is more suitable to use non-extensive statistical mechanics instead of the usual Gibbs-Boltzmann ones. In this work, the black hole entropy is derived based on Tsallis statistical mechanics, one of well-known non-extensive statistical mechanics. It is found that the black hole entropy gets a modification due to non-extensivity. By using such an entropy, the black hole can be stabilized due to the non-extensivity, and the bound on the non-extensive parameter is also determined.
45 pages, 7 figures
References in corpus (75)
- Microscopic Origin of the Bekenstein-Hawking Entropy
- Black hole chemistry: thermodynamics with Lambda
- Logarithmic correction to the Bekenstein-Hawking entropy
- Black hole thermodynamical entropy
- The Area of a Rough Black Hole
- Black hole entropy from Quantum Geometry
- Quantum Tunneling Beyond Semiclassical Approximation
- Quantum Tunneling and Back Reaction
- Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactions
- Holographic dark energy through Tsallis entropy
- Rényi entropy and the thermodynamic stability of black holes
- Early and late universe holographic cosmology from a new generalized entropy
- Modified Friedmann Equations from Tsallis Entropy
- Tsallis' entropy maximization procedure revisited
- Minimum Length from Quantum Mechanics and Classical General Relativity
- A q-parameter bound for particle spectra based on black hole thermodynamics with Rényi-entropy
- Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasinormal modes
- The nonextensive parameter and Tsallis distribution for self-gravitating systems
- Lessons from Classical Gravity about the Quantum Structure of Spacetime
- Zeroth Law compatibility of non-additive thermodynamics
- Behavior of quasinormal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity
- Photon orbits and thermodynamic phase transition of -dimensional charged AdS black holes
- Area-law versus Rényi and Tsallis black hole entropies
- Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions
- Thermodynamics, stability and Hawking-Page transition of Kerr black holes from Rényi statistics
- Modified cosmology through nonextensive horizon thermodynamics
- Behavior of Quasinormal Modes and high dimension RN-AdS Black Hole phase transition
- Gravothermal Catastrophe and Generalized Entropy of Self-Gravitating Systems
- Thermodynamics and Van der Waals Phase Transition of Charged Black Holes in Flat Space via Rényi Statistics
- Equivalence of the four versions of Tsallis statistics
- Thermal Image and Phase Transitions of Charged AdS Black Holes using Shadow Analysis
- An Operational Approach To Black Hole Entropy
- Alternative entropies and consistent black hole thermodynamics
- Ideal gas in nonextensive optimal Lagrange multipliers formalism
- Gravothermal Catastrophe and Tsallis' Generalized Entropy of Self-Gravitating Systems III. quasi-equilibrium structure using normalized q-values
- New explanation for accelerated expansion and flat galactic rotation curves
- New entropies, black holes, and holographic dark energy
- Probing Phase Structure of Black Holes with Lyapunov Exponents
- Thermodynamics and Phase Transition of Spherically Symmetric Black Hole in de Sitter Space from Rényi Statistics
- Nonextensive Black Hole Entropy and Quantum Gravity Effects at the Last Stages of Evaporation
- Self-gravitating Stellar Systems and Non-extensive Thermostatistics
- Relativity, nonextensivity, and extended power law distributions
- Circular orbit of a test particle and phase transition of a black hole
- Signature of the black hole phase transition in quasinormal modes
- Ideal Gas in a strong Gravitational field: Area dependence of Entropy
- Solid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the Rényi Extended Phase Space Approach
- Effective thermodynamical system of Schwarzschild-de Sitter black holes from Rényi statistics
- Lyapunov Exponents and Phase Transitions of Born-Infeld AdS Black Holes
- Generalized Uncertainty Principle Impact on Nonextensive Black Hole Thermodynamics
- Gravothermal Catastrophe and Tsallis' Generalized Entropy of Self-Gravitating Systems II. Thermodynamic Properties of Stellar Polytrope
- On the generalized entropy pseudoadditivity for complex systems
- Equilibrium Temperature for Black Holes with Nonextensive Entropy
- Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles
- Emergent Phase, Thermodynamic Geometry and Criticality of Charged Black Holes from Rényi Statistics
- Stellar polytropes and Navarro-Frenk-White halo models: comparison with observations
- Area scaling entropies for gravitating systems
- Condensation of an ideal gas with intermediate statistics on the horizon
- Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes
- Thermodynamics of Asymptotically de-Sitter Black Hole in dRGT Massive Gravity from Rényi entropy
- Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame
- Lagrangian formulation of the Tsallis entropy
- Entropy of a box of gas in an external gravitational field revisited
- Understanding Gravitational Entropy of Black Holes: A New Proposal via Curvature Invariants
- Generalized Entropy Implies Varying-G: Horizon Area Dependent Field Equations and Black Hole-Cosmology Coupling
- Thermodynamics of Black Holes with Rényi Entropy from Classical Gravity
- Comment on "Black Hole Entropy: A Closer Look"
- Nonextensive statistics of relativistic ideal gas
- Nonextensivity and q-distribution of a relativistic gas under an external electromagnetic field
- The limit behavior of the evolution of Tsallis entropy in self-gravitating systems
- Thermal leptogenesis in nonextensive cosmology
- Quantum statistical mechanics near a black hole horizon
- A shell of Bosons in Spherically Symmetric spacetimes
- Reconciling fractional entropy and black hole entropy compositions
- A class of energy based ensembles in Tsallis statistics
- -Equilibrium of Gas in Spacetime of Multi-horizon Black Holes