Statistical Power Law due to Reservoir Fluctuations and the Universal Thermostat Independence Principle
arXiv:1409.5975 · doi:10.3390/e16126497
Abstract
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed automatically by an equipartition relation, while the q-parameter is related to the scaled variance and to the expectation value of the particle number. For the binomial distribution q is smaller, for the negative binomial q is larger than one. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the canonical expansion. For general systems the average phase-space volume ratio expanded to second order delivers a q parameter related to the heat capacity and to the variance of the temperature. However, q differing from one leads to non-additivity of the Boltzmann-Gibbs entropy. We demonstrate that a deformed entropy, K(S), can be constructed and used for demanding additivity. This requirement leads to a second order differential equation for K(S). Finally, the generalized q-entropy formula contains the Tsallis, Renyi and Boltzmann-Gibbs-Shannon expressions as particular cases. For diverging temperature variance we obtain a novel entropy formula.
arXiv commentTalk given by T.S.Biro at Sigma Phi 2014, Rhodos, Greece
References in corpus (48)
- Superstatistics
- Interpretation of the nonextensitivity parameter in some applications of Tsallis statistics and Lévy distributions
- Centrality dependence of , K, p production in Pb-Pb collisions at = 2.76 TeV
- Dynamical foundations of nonextensive statistical mechanics
- Centrality dependence of charged particle production at large transverse momentum in Pb-Pb collisions at TeV
- Axioms and uniqueness theorem for Tsallis entropy
- Thermostatistics of overdamped motion of interacting particles
- Non-Extensive Approach to Quark Matter
- Power laws in elementary and heavy-ion collisions - A story of fluctuations and nonextensivity?
- General pseudoadditivity of composable entropy prescribed by existence of equilibrium
- Tsallis Fits to pT Spectra and Multiple Hard Scattering in pp Collisions at the LHC
- Superstatistics, thermodynamics, and fluctuations
- Power-law tails from multiplicative noise
- Particle Number Fluctuations in Canonical Ensemble
- Zeroth Law compatibility of non-additive thermodynamics
- Generalized entropies from first principles
- Tsallis Fits to p_T Spectra for pp Collisions at LHC
- When is a quantity additive, and when is it extensive?
- Charged hadron multiplicity fluctuations in Au+Au and Cu+Cu collisions from sqrt(s_NN) = 22.5 to 200 GeV
- Consequences of temperature fluctuations in observables measured in high energy collisions
- Non-extensive Boltzmann Equation and Hadronization
- Thermodynamic Derivation of the Tsallis and Rényi Entropy Formulas and the Temperature of Quark-Gluon Plasma
- Generalised Tsallis Statistics in Electron-Positron Collisions
- Two generalizations of the Boltzmann equation
- Microcanonical Jet-fragmentation in proton-proton collisions at LHC Energy
- Dynamical Correlations as Origin of Nonextensive Entropy
- New Entropy Formula with Fluctuating Reservoir
- Power Law in Micro-Canonical Ensemble with Scaling Volume Fluctuations
- Cooper-Frye Formula and Non-extensive Coalescence at RHIC Energy
- Ideal gas provides q-entropy
- Nonuniqueness of Canonical Ensemble Theory arising from Microcanonical Basis
- Particle Number Fluctuations in Relativistic Bose and Fermi Gases
- Microscopic Origin of Non-Gaussian Distributions of Financial Returns
- Abstract composition rule for relativistic kinetic energy in the thermodynamical limit
- Microcanonical Ensemble Extensive Thermodynamics of Tsallis Statistics
- Justification of Power-Law Canonical Distributions Based on Generalized Central Limit Theorem
- Identity Method for Particle Number Fluctuations and Correlations
- Macroscopic thermodynamics of equilibrium characterized by power-law canonical distributions
- Fluctuations of rare particles as a measure of chemical equilibration
- Limiting temperature from a parton gas with power-law tailed distribution
- Strongly Intensive Measures for Transverse Momentum and Particle Number Fluctuations
- Generalized thermodynamic uncertainty relations
- On the origin of power-laws in equilibrium
- Nonadditive thermostatistics and thermodynamics
- Power-law tailed spectra from equilibrium
- Semi-Inclusive Distributions in Statistical Models
- Statistical Power-Law Spectra due to Reservoir Fluctuations
- Non-extensive equilibration in relativistic matter
Cited by in corpus (22)
- From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy and collisions
- Radial Flow in Non-Extensive Thermodynamics and Study of Particle Spectra at LHC in the Limit of Small
- Systematic Analysis of the Non-extensive Statistical Approach in High Energy Particle Collisions - Experiment vs. Theory
- Time Evolution of Temperature Fluctuation in a Non-Equilibrated System
- Application of the Non-extensive Statistical Approach to High Energy Particle Collisions
- Physics-inspired analysis of the two-class income distribution in the USA in 1983-2018
- Quasi-power laws in multiparticle production processes
- Approach of complexity in nature: Entropic nonuniqueness
- Self-consistent thermodynamics for the Tsallis statistics in the grand canonical ensemble: Nonrelativistic hadron gas
- Axiomatic nonextensive statistics at NICA energies
- Non-extensive statistical distributions of charmed meson production in Pb-Pb and pp() collisions
- Rescaling the nonadditivity parameter in Tsallis thermostatistics
- Nuclear and Quark Matter at High Temperature
- Entropy Production During Hadronization of a Quark-Gluon Plasma
- Near and Far from Equilibrium Power-Law Statistics
- Non-extensive Motivated Parton Fragmentation Functions
- Equilibrium distributions in entropy driven balanced processes
- Particle yields from numerical simulations
- How far can we see back in time in high-energy collisions using charm hadrons?
- Emergent family of Tsallis entropies from the -deformed combinatorics
- Random statistical analysis of transverse momentum spectra of strange particles and dependence of related parameters on centrality in high energy collisions at the LHC
- Thermodynamic and hydrodynamic characteristics of interacting system formed in relativistic heavy ion collisions