New Entropy Formula with Fluctuating Reservoir

Abstract

Finite heat reservoir capacity and temperature fluctuations lead to modification of the well known canonical exponential weight factor. Requiring that the corrections least depend on the one-particle energy, we derive a deformed entropy, K(S). The resulting formula contains the Boltzmann-Gibbs, the Renyi and the Tsallis formulas as particular cases. For extreme large fluctuations (compared to the Gaussian case) a new, parameter-free entropy - probability relation emerges. This formula and the corresponding canonical equilibrium distribution are nearly Boltzmannian for high probability, but deviate from the classical result for low probability. In the extreme large fluctuation limit the canonical distribution resembles for low probability the cumulative Gompertz distribution.

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• Microcanonical Jet-fragmentation in proton-proton collisions at LHC Energy
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• Application of the Non-extensive Statistical Approach to High Energy Particle Collisions
• Some intriguing aspects of multiparticle production processes
• Different Non-extensive Models for heavy-ion collisions
• Quasi-power laws in multiparticle production processes
• Axiomatic nonextensive statistics at NICA energies
• Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems
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• On Statistical Properties of Jizba-Arimitsu Hybrid Entropy
• Rescaling the nonadditivity parameter in Tsallis thermostatistics
• On the uniqueness theorem for pseudo-additive entropies
• Nuclear and Quark Matter at High Temperature
• Role of chemical potential at kinetic freeze-out using Tsallis non-extensive statistics in proton-proton collisions at the Large Hadron Collider
• From Rényi Entropy Power to Information Scan of Quantum States
• Understanding the negative binomial multiplicity fluctuations in relativistic heavy ion collisions
• The Effects of the Tsallis Entropy in the Proton Internal Pressure
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• Effect of event classification on the Tsallis-thermometer