Quark-gluon plasma connected to finite heat bath

Abstract

Abstract. We derive entropy formulas for finite reservoir systems, S q , from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result interprets thermodynamically the subsystem temperature, T 1, 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. MotivationA nonlinear entropy formula has been suggested by Rényi long ago and been applied to several areas in physics [1][2][3][4][5][6][7]. Another formula, the Tsallis entropy, has more recently been promoted as the keystone for a generalized thermodynamics, treating correlated physical systems [8][9][10][11] with intrinsic, either statistical or dynamical fluctuations [12,13]. A respectable amount of papers applying this idea to one or the other area in physics appeared [14][15][16][17][18][19]. Since from this entropy the canonical energy distribution is power law tailed in place of the Boltzmann-Gibbs exponential, numerous high-energy distributions have been fitted using the Tsallis formula [12,[20][21][22][23][24][25][26][27][28]. Its independence from the thermostat and the thermodynamical foundation behind the use of such a formula are interesting questions. This is even true for such a simple system like the ideal gas in a generalized form [29], which can also provide power law distribution [30][31][32][33]. It has been recently proven that -considering in the traditional way-the thermodynamical and conditional probability of an ideal gas and its part, respectively, provide Rényi and Tsallis q-entropy formulas [34].In our earlier works we investigated some general mathematical properties of alternative entropy formulas via their pairwise composition rules, and established that a scaled repetition of an arbitrary composition rule leads to an associative asymptotic composition rule of large subsystems [35]. All such rules are uniquely defined by a strict monotonic function, their formal logarithm denoted by L (see eq. (3)). Recently we have also observed that -in a e-mail: Barnafoldi.Gergely@wigner.mta.hu connection to the zero-th law of thermodynamics-the factorizability condition on the common entropy maximum [36] allows only for such rules [37]. We seek in this paper for the thermodynamical meaning of the q parameter generalizing the classical entropy formula, valid for q = 1. Some q = 1 parameter were calculated theoretically [38][39][40]. Classical thermodynamical and statistical fundamentsThe total entropy is expressed by the Planck formula,withN i !, considering altogether N states in r classes and in each class N i indistinguish...

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