Quark-gluon plasma connected to finite heat bath

We derive entropy formulas for finite reservoir systems, Sq, from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result interprets thermodynamically the subsystem temperature, T1, and the index q in terms of the temperature, T , entropy, S , and heat capacity, C of the reservoir as $ T_1=T \exp(-S/C)$ and $ q=1-1/C$ . In the infinite C limit, irrespective of the value of S , the Boltzmann-Gibbs approach is fully recovered. We apply this framework for the experimental determination of the original temperature of a finite thermostat, T , from the analysis of hadron spectra produced in high-energy collisions, by analyzing frequently considered simple models of the quark-gluon plasma.

[1]  J. Cleymans,et al.  The Tsallis distribution in proton?proton collisions at $\sqrt{s}$ = 0.9 TeV at the LHC , 2011, 1110.5526.

[2]  A G Bashkirov.  Comment on "Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions". , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Jincan Chen,et al.  q-generalized Bose-Einstein condensation based on Tsallis entropy , 2002 .

[4]  P. Henrard,et al.  Measurement of J/psi production in $pp$ collisions at $s=2.76$ TeV , 2012, 1212.1045.

[5]  A. Fulop,et al.  Towards the Equation of State of Classical SU(2) Lattice Gauge Theory , 2001, hep-ph/0107008.

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

[7]  V. V. Begun,et al.  Particle number fluctuations in relativistic Bose and Fermi gases , 2006 .

[8]  R. Bellwied,et al.  Statistical hadronization phenomenology in K/π fluctuations at ultra-relativistic energies , 2009, 1001.0087.

[9]  C. Tsallis.  Nonextensive Statistical Mechanics and Nonlinear Dynamics , 2008 .

[10]  T S Biró,et al.  Nonextensive boltzmann equation and hadronization. , 2005, Physical review letters.

[11]  On the limiting cases of nonextensive thermostatistics , 2006, cond-mat/0611068.

[12]  G. Wilk,et al.  Multiplicity fluctuations in high energy hadronic and nuclear collisions , 2004 .

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

[14]  A. Parvan,et al.  Rényi statistics in equilibrium statistical mechanics , 2009, 0910.3062.

[15]  A M Scarfone,et al.  Two-parameter deformations of logarithm, exponential, and entropy: a consistent framework for generalized statistical mechanics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[17]  G. Wilk,et al.  On the possibility of q-scaling in high energy production processes , 2012, 1203.6787.

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

[19]  Peter Hänggi,et al.  Finite bath fluctuation theorem. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  E. Lutz.  Anomalous diffusion and Tsallis statistics in an optical lattice , 2003 .

[21]  T. S. Biro,et al.  Abstract composition rule for relativistic kinetic energy in the thermodynamical limit , 2008, 0809.4675.

[22]  J. Cleymans,et al.  Near-thermal equilibrium with Tsallis distributions in heavy ion collisions , 2008, 0812.1471.

[23]  E. K. Lenzi,et al.  Statistical mechanics based on Renyi entropy , 2000 .

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

[25]  P. Douglas,et al.  Tunable Tsallis distributions in dissipative optical lattices. , 2006, Physical review letters.

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

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

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

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

[30]  A. M. Mathai,et al.  On generalized distributions and pathways , 2008 .

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

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

[33]  Constantino Tsallis,et al.  Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  C. Tsallis,et al.  The role of constraints within generalized nonextensive statistics , 1998 .

[35]  J. Cleymans,et al.  Relativistic thermodynamics: Transverse momentum distributions in high-energy physics , 2012, The European Physical Journal A.

[36]  A non-extensive equilibrium analysis of π+ pT spectra at RHIC , 2010, 1001.3136.

[37]  A. R. Plastino,et al.  Tsallis entropy and Jaynes' Information Theory formalism , 1999 .

[38]  T. Biró,et al.  EPJ manuscript No. (will be inserted by the editor) Non-Extensive Approach to Quark Matter , 2022 .

[39]  T. Biró,et al.  Thermodynamics of composition rules , 2010 .

[40]  C. Tsallis.  Nonextensive statistics: theoretical, experimental and computational evidences and connections , 1999, cond-mat/9903356.

[41]  Funabashi,et al.  Quantum entanglement inferred by the principle of maximum nonadditive entropy , 1999 .

[42]  T. Biró,et al.  Transverse hadron spectra from a stringy quark matter , 2009 .

[43]  P. Jizba,et al.  Observability of Rényi's entropy. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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