Boltzmann-Gibbs entropy is sufficient but not necessary for the likelihood factorization required by Einstein
arXiv:1407.6052 · doi:10.1209/0295-5075/110/30005
Abstract
In 1910 Einstein published a crucial aspect of his understanding of Boltzmann entropy. He essentially argued that the likelihood function of any system composed by two probabilistically independent subsystems {\it ought} to be factorizable into the likelihood functions of each of the subsystems. Consistently he was satisfied by the fact that Boltzmann (additive) entropy fulfills this epistemologically fundamental requirement. We show here that entropies (e.g., the -entropy on which nonextensive statistical mechanics is based) which generalize the BG one through violation of its well known additivity can {\it also} fulfill the same requirement. This fact sheds light on the very foundations of the connection between the micro- and macro-scopic worlds.
arXiv comment5 pages including 2 figures
References in corpus (35)
- Area laws for the entanglement entropy - a review
- Black hole thermodynamical entropy
- Transverse-momentum and pseudorapidity distributions of charged hadrons in pp collisions at sqrt(s) = 7 TeV
- Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
- Production of pions, kaons and protons in pp collisions at GeV with ALICE at the LHC
- Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
- Measurement of neutral mesons in p+p collisions at sqrt(s) = 200 GeV and scaling properties of hadron production
- Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
- Identified charged hadron production in p+p collisions at sqrt(s)=200 and 62.4 GeV
- Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
- Transverse momentum spectra of charged particles in proton-proton collisions at GeV with ALICE at the LHC
- Entropies based on fractional calculus
- Thermostatistics of overdamped motion of interacting particles
- Structure of Stochastic Dynamics near Fixed Points
- Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
- Tsallis Fits to pT Spectra and Multiple Hard Scattering in pp Collisions at the LHC
- Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
- Generalization of symmetric -stable Lévy distributions for
- Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
- Statistical Entropy of De Sitter Space
- Group entropies, correlation laws and zeta functions
- Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics
- Tsallis statistics as a tool for studying interstellar turbulence
- A General Nonlinear Fokker-Planck Equation and its Associated Entropy
- Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics
- Influence of the interaction range on the thermostatistics of a classical many-body system
- Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. III: potential function in local stochastic dynamics and in steady state of Boltzmann-Gibbs type distribution function
- How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems
- Beyond Itô versus Stratonovich
- Antiproton-to-Proton Ratios for ALICE Heavy-Ion Collisions
- Reply to Comment on "Towards a large deviation theory for strongly correlated systems"
- Two-parameter generalization of the logarithm and exponential functions and Boltzmann-Gibbs-Shannon entropy
- Effective temperature for black holes
- Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription
- Possible Implication of a Single Nonextensive Distribution for Hadron Production in High-Energy Collisions