Consequences of temperature fluctuations in observables measured in high-energy collisions

Wilk, G.; Włodarczyk, Z.

doi:10.1140/epja/i2012-12161-y

Cited by 93 publications

(121 citation statements)

References 113 publications

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“…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.…”

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confidence: 99%

Quark-gluon plasma connected to finite heat bath

2013

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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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confidence: 99%

Quark-gluon plasma connected to finite heat bath

2013

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“…(known as preferential attachment in networks [22,76,77] (it is worth recalling here that this very same form, T (E) = T 0 + (1 − q)E, also appears in [39] within a Fokker-Planck dynamics applied to the thermalization of quarks in a quark-gluon plasma by collision processes)),…”

Section: Log-periodic Oscillations In a Tsallis Distribution: Complexmentioning

confidence: 97%

“…As shown in [29] (cf., also, [22,23,[78][79][80]), the nonextensivity parameter q can be treated as a measure of the thermal bath heat capacity C with:…”

Section: Complex Heat Capacitymentioning

confidence: 99%

Tsallis Distribution Decorated with Log-Periodic Oscillation

Wilk

Włodarczyk

2015

Entropy

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In many situations, in all branches of physics, one encounters the power-like behavior of some variables, which is best described by a Tsallis distribution characterized by a nonextensivity parameter q and scale parameter T . However, there exist experimental results that can be described only by a Tsallis distributions, which are additionally decorated by some log-periodic oscillating factor. We argue that such a factor can originate from allowing for a complex nonextensivity parameter q. The possible information conveyed by such an approach (like the occurrence of complex heat capacity, the notion of complex probability or complex multiplicative noise) will also be discussed.

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“…Complex systems with multiple time and length scales occur frequently in many areas of physics and interdisciplinary fields, such as turbulence [1], random-matrix theory [2], highenergy collision physics [3,4], and econophysics [5], to mention only a few. One common feature among many such systems is the appearance of probability distributions that deviate considerably from what one would expect (say, Gaussian or exponential behavior) on the basis of standard equilibrium statistical mechanics arguments.…”

Section: Introductionmentioning

confidence: 99%

Maximum entropy approach toH-theory: Statistical mechanics of hierarchical systems

2018

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A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem-representing the region where the measurements are made-in contact with a set of 'nested heat reservoirs' corresponding to the hierarchical structure of the system. The probability distribution function (pdf) of the fluctuating temperatures at each reservoir, conditioned on the temperature of the reservoir above it, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H-functions. The distribution of states of the small subsystem is then computed by averaging the quasi-equilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H-functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017)] from a stochastic dynamical approach to the problem.

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Consequences of temperature fluctuations in observables measured in high-energy collisions

Cited by 93 publications

References 113 publications

Quark-gluon plasma connected to finite heat bath

Quark-gluon plasma connected to finite heat bath

Tsallis Distribution Decorated with Log-Periodic Oscillation

Maximum entropy approach toH-theory: Statistical mechanics of hierarchical systems

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