Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then established. In the classical case, Galilean invariance...

A direct numerical simulation of a turbulent flow field with a lattice BGK method is presented. A spatial coarse graining of the numerical results is compared with the expected LBGK dynamics for a flow field on a reduced lattice size. This comparison permits to exhibit subgrid properties of the...

The exact forms of the degenerate Maxwell–Boltzmann (MB), Bose–Einstein (BE) and Fermi–Dirac (FD) entropy functions, derived by Boltzmann's principle without the Stirling approximation [R.K. Niven, Physics Letters A, 342(4) (2005) 286], are further examined. Firstly, an apparent paradox in...

We study the model of interacting agents proposed by Chakraborti and Chakrabarti [Eur. Phys. J. B 17 (2000) 167] that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation.

The Burnett constitutive equations for the dynamic pressure, heat flux and pressure deviator of a relativistic gas are calculated from a moment closure of the Anderson and Witting model equation. The transport coefficients obtained are compared with those that follow by the use of the full...

We derive the free energy of the chiral Potts model by the infinite lattice “inversion relation” method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice functional relations, we find that...

Effects of the averaging over disorder realizations (samples) on the phase behavior are analyzed in terms of the mean field approximation for the random field Ising model with infinite range interactions. It is found that the averaging is equivalent to a drastic modification in the statistics of...

In this paper, we analyze the process of money creation in a credit economy. We start from the consideration that the traditional money multiplier is a poor description of this process and present an alternative and dynamic approach that takes into account the heterogeneity of agents in the...

Recently the thermostatted kinetic framework has been proposed as mathematical model for studying nonequilibrium complex systems constrained to keep constant the total energy. The time evolution of the distribution function of the system is described by a nonlinear partial integro-differential...

This discussion paper critically reviews a new book by Aoki and Yokishawa and presents some of the techniques adopted by the authors as a new approach to the foundations of macroeconomics. The paper discusses some of the main techniques of statistical mechanics relevant in this context, namely...