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Basic equations of nonequilibrium thermo field dynamics of dense quantum systems are presented. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev. Hydrodynamic equations have been obtained in thermo field representation. Two levels of the description of kinetics and hydrodynamics of a dense nuclear matter are considered. The first one is a quantum system with strongly coupled states, the second one is a quarkgluon plasma. Generalized transfer equations of a consistent description of kinetics and hydrodynamics have been obtained, as well as limiting cases are considered.

An analytical expression of probability density function (PDF) of accelerations in turbulence is derived with the help of the statistics based on generalized entropy (the Tsallis entropy or the Rényi entropy). It is revealed that the derived PDF explains the one obtained by Bodenschatz et al. in the measurement of fluid particle accelerations in fully developed turbulence at R λ = 970 . 47.27.-i, 47.53.+n, 47.52.+j, 05.90.+m The multifractal analysis of turbulence by the statistics based on the generalized entropy of Rényi's or of Tsallis' has been developed by the present authors [1][2][3][4][5][6][7][8][9]. Similarly to the usual thermodynamic entropy, the Rényi entropy [10] is of an extensive character, whereas the Tsallis entropy [11-13] is non-extensive. The multifractal analysis belongs to the line of study based on a kind of ensemble theoretical approaches that, starting from the log-normal model [14][15][16], continues with the β-model [17], the p-model [18,19], the 3D binomial Cantor set model [20] and so on. After a rather preliminary investigation of the p-model [1], we developed further to derive the analytical expression for the scaling exponents of velocity structure function [2][3][4][5], and to determine the probability density function (PDF) of velocity fluctuations [5][6][7][8] and of velocity derivative [9] by a self-consistent statistical mechanical approach. Key words: multifractal analysis, fully developed turbulence, PDF of fluid particle accelerations, Rényi entropy, Tsallis entropy PACS:In this paper, we will derive the formula for the PDF of the accelerations of a fluid particle in fully developed turbulence by means of the multifractal analysis. With the theoretical PDF, we will analyze the PDF of accelerations at R λ = 970 (the Taylor microscale Reynolds number) obtained in the Lagrangian measurement *

Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.

Out of thermal equilibrium state, the vacuum is unstable and evolves in time. Consequently, the annihilation operators associated with the unstable vacuum depend on time. This dissipative time-evolution of quantum systems can be systematically treated, within the canonical operator formalism referred to as non-equilibrium thermo-field dynamics. Given is an alternative route to derive the time-dependent annihilation operators within the formalism. As an example, time-dependent annihilation operators for the systems of bosonic and fermionic semi-free fields are derived.