New Entropy Formula with Fluctuating Reservoir

Finite heat reservoir capacity, C, and temperature fluctuation, ΔT/T, lead to modifications of the well known canonical exponential weight factor. Requiring that the corrections least depend on the one-particle energy, ω, we derive a deformed entropy, K(S). The resultingformula contains the Boltzmann–Gibbs, Renyi, and Tsallis formulas as particular cases. For extreme large fluctuations, in the limit CΔT2/T2→∞, a new parameter-free entropy–probability relation is gained. The corresponding canonical energy distribution is nearly Boltzmannian for high probability, but for low probability approaches the cumulative Gompertz distribution. The latter is met in several phenomena, like earthquakes, demography, tumor growth models, extreme value probability, etc.

[1]  T S Biró,et al.  Zeroth law compatibility of nonadditive thermodynamics. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Włodarczyk,et al.  Interpretation of the nonextensivity parameter q in some applications of tsallis statistics and Levy distributions , 2000, Physical review letters.

[3]  M. P. Almeida.  Generalized entropies from first principles , 2001 .

[4]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[5]  B. H. Lavenda,et al.  COMMENTS ON “THERMODYNAMIC UNCERTAINTY RELATIONS” BY J. UFFINK AND J. VAN LITH , 2000 .

[6]  T. Biró,et al.  Ideal gas provides q-entropy , 2012, 1211.5284.

[7]  K. Obara,et al.  Characteristics of short‐term slow slip events estimated from deep low‐frequency tremors in Shikoku, Japan , 2010 .

[8]  T. Biró.  Is There a Temperature , 2011 .

[9]  J. Uffink,et al.  Thermodynamic Uncertainty Relations Again: A Reply to Lavenda , 2001 .

[10]  Jos Uffink,et al.  Thermodynamic Uncertainty Relations , 1998 .

[11]  G. Wilk,et al.  Power laws in elementary and heavy-ion collisions , 2008, 0810.2939.

[12]  Thomas Oikonomou,et al.  Comment on"Tsallis power laws and finite baths with negative heat capacity"[Phys. Rev. E 88, 042126 (2013)] , 2013, 1310.5556.

[13]  T. S. Biro,et al.  Generalised Tsallis Statistics in Electron-Positron Collisions , 2011, 1101.3023.

[14]  Péter Ván,et al.  Quark-gluon plasma connected to finite heat bath , 2013 .

[15]  V. V. Begun,et al.  Particle number fluctuations in a canonical ensemble , 2004 .

[16]  Michele Campisi,et al.  On the origin of power laws in equilibrium , 2012 .

[17]  V. V. Begun,et al.  Power law in a microcanonical ensemble with scaling volume fluctuations , 2008 .

[18]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[19]  K. Grebieszkow,et al.  Strongly intensive measures for transverse momentum and particle number fluctuations , 2013, 1309.7878.

[20]  G. Wilk,et al.  Consequences of temperature fluctuations in observables measured in high-energy collisions , 2012, 1203.4452.

[21]  G. Wilk,et al.  Equivalence of volume and temperature fluctuations in power-law ensembles , 2010, 1006.3657.

[22]  A new magnitude-frequency relation , 1978 .

[23]  Grzegorz Wilk,et al.  The imprints of superstatistics in multiparticle production processes , 2011, 1110.4220.

[24]  Inder Jeet Taneja,et al.  On Generalized Information Measures and Their Applications , 1989 .

[25]  M. I. Gorenstein,et al.  Identity method for particle number fluctuations and correlations , 2011, 1106.4473.

[26]  G. Barnafoldi,et al.  Microcanonical jet-fragmentation in proton–proton collisions at LHC energy , 2012, 1204.1508.

[27]  V. V. Begun,et al.  Semi-inclusive distributions in statistical models , 2009 .

[28]  Constantino Tsallis,et al.  Introduction to Nonextensive Statistical Mechanics and Thermodynamics , 2003 .

[29]  Remo Guidieri.  Res , 1995, RES: Anthropology and Aesthetics.

[30]  Albert E. Casey,et al.  The Experimental Alteration of Malignancy with an Homologous Mammalian Tumor Material: I. Results with Intratesticular Inoculation , 1934 .

[31]  Derivation of relativistic hydrodynamic equations consistent with relativistic Boltzmann equation by renormalization-group method , 2012, 1206.1929.

[32]  S. Jeon,et al.  Fluctuations of rare particles as a measure of chemical equilibration , 2001, nucl-th/0105035.

[33]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[34]  C. Tsallis.  Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World , 2009 .