Generalized entropies from first principles

Abstract

We present a derivation of power law canonical distributions from first principle statistical mechanics, including the exponential distribution as a It is presented a derivation of power law canonical distributions from first principle statistical mechanics, including the exponential distribution as a particular case. It is shown that these distributions arise naturally, and that the heat capacity of the heat bath is the condition that determines its type. As a consequence, it is given a physical interpretation for the parameter $q$ of the generalized entropy.

3 pages

Cited by in corpus (53)

• Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactions
• Power laws in elementary and heavy-ion collisions - A story of fluctuations and nonextensivity?
• The nonextensive parameter and Tsallis distribution for self-gravitating systems
• A nonextensive entropy approach to solar wind intermittency
• Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions
• Coarse-grained distributions and superstatistics
• Nonextensive theory of dark matter and gas density profiles
• Thermodynamic Derivation of the Tsallis and Rényi Entropy Formulas and the Temperature of Quark-Gluon Plasma
• Equivalence of the four versions of Tsallis statistics
• On the meaning of Tsallis functional in astrophysics
• Tsallis Distribution Decorated With Log-Periodic Oscillation
• Tsallis thermostatistics for finite systems: a Hamiltonian approach
• Finite Bath Fluctuation Theorem
• Disentangling random thermal motion of particles and collective expansion of source from transverse momentum spectra in high energy collisions
• Statistical Power Law due to Reservoir Fluctuations and the Universal Thermostat Independence Principle
• Thermodynamics with long-range interactions: from Ising models to black-holes
• New Entropy Formula with Fluctuating Reservoir
• An extended-phase-space dynamics for the generalized nonextensive thermostatistics
• Statistical Mechanics in the Extended Gaussian Ensemble
• Tsallis distribution with complex nonextensivity parameter q
• Ideal gas provides q-entropy
• What does the nonextensive parameter q stand for in self-gravitating systems ?
• Classical small systems coupled to finite baths
• Quasi-power laws in multiparticle production processes
• Dark matter density profiles: A comparison of nonextensive theory with N-body simulations
• Extended Gaussian ensemble or q-statistics in hadronic production processes?
• Thermodynamics with generalized ensembles: The class of dual orthodes
• An additive variant of Tsallis generalized entropy
• On the Limiting Cases of Nonextensive Thermostatistics
• Tsallis meets Boltzmann: q-index for a finite ideal gas and its thermodynamic limit
• Quasicanonical Gibbs distribution and Tsallis nonextensive statistics
• A new form of Tsallis distribution based on the probabilistically independent postulate
• Derivation of Tsallis statistics from dynamical equations for a granular gas
• On the Derivation of power-law distributions within standard statistical mechanics
• Ricci curvature, isoperimetry and a non-additive entropy
• On the origin of power-laws in equilibrium
• Fluctuation of energy in the generalized thermostatistics
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Tsallis' deformation parameter q quantifies the classical-quantum transition
• Numerical calculation of the energy relative fluctuation for a system in contact with a finite heat bath
• Possible dynamics of the Tsallis distribution from a Fokker-Planck equation (I)
• Stochastic thermodynamics and fluctuation theorems for non-linear systems
• Model-free derivations of the Tsallis factor: constant heat capacity derivation
• Possible canonical distributions for finite systems with nonadditive energy
• Nonextensivity and q-distribution of a relativistic gas under an external electromagnetic field
• On the extended Kolmogorov-Nagumo information-entropy theory, the q -> 1/q duality and its possible implications for a non-extensive two dimensional Ising model
• A generalized thermodynamics for power-law statistics
• Thermodynamics arising from Tsallis' thermostatistics
• Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics
• Chiral phase transition in the linear sigma model within Hartree factorization in the Tsallis nonextensive statistics
• Emergent family of Tsallis entropies from the $q$-deformed combinatorics
• The anomalous distributions and Soret coefficient in a nonequilibrium colloid system
• Ising model in the Rényi statistics: the finite size effects