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Register a new userStatistical Ensembles with Fluctuating Extensive Quantities
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We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy fluctuations on multiplicity fluctuations in limited segments of momentum space for a classical ultra-relativistic gas is considered.
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A Monte Carlo event generator has been developed assuming thermal production of hadrons. The system under consideration is sampled grand canonically in the Boltzmann approximation. A re-weighting scheme is then introduced to account for conservation of charges (baryon number, strangeness, electric charge) and energy and momentum, effectively allowing for extrapolation of grand canonical results to the microcanonical limit. This method has two strong advantages compared to analytical approaches and standard microcanonical Monte Carlo techniques, in that it is capable of handling resonance decays as well as (very) large system sizes.
The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplaces asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. Gram-Charlier expansion allows additionally for calculation of finite volume corrections. Analytical formulas are presented for inclusion of resonance decay and finite acceptance effects directly into the system partition function. This paper consolidates and extends previously published results of current investigation into properties of statistical ensembles.
We present a semi-analytic approach to forward-backward multiplicity correlations in ultra-relativistic nuclear collisions, based on particle emission from strings with fluctuating end-points. We show that with the constraints from rapidity spectra, one can obtain bounds for the magnitude of the standard measures of the forward-backward fluctuations. The method is generic under the assumption of independent production from sources. For definiteness, we use the wounded quark model for Au+Au and d+Au collisions at the energy of $sqrt{s_{NN}}=200$ GeV.
We review the evolution of some statistical and thermodynamical quantities measured in difference sizes of high-energy collisions at different energies. We differentiate between intensive and extensive quantities and discuss the importance of their distinguishability in characterizing possible critical phenomena of nuclear collisions at various energies with different initial conditions.
Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is formulated by putting an emphasis on non-linearity and causality. As a consequence of causality, dissipative currents become dynamical variables and noises appeared in an integral form of constitutive equations should be colored ones from fluctuation-dissipation relations. Nevertheless noises turn out to be white ones in its differential form when noises are assumed to be Gaussian. The obtained ifferential equations are very useful in numerical implementation of relativistic fluctuating hydrodynamics.
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