A derivation is given of the Boltzmann–Vlasov equation beginning from multiple scattering considerations. The motivation for the discussion, which is purely pedagogical in nature, is the current interest in understanding the origins of transport equations in terms of rigorous field-theory descriptions, or, as in this case, exact nonrelativistic formulations.

We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self tim...

Thermophoresis, also termed thermal diffusion or the Soret effect, moves particles along temperature gradients. For particles in liquids, the effect lacks a theoretical explanation. We present experimental results at moderate thermal gradients: (i) Thermophoretic depletion of 200 nm polystyrene spheres in water follows an exponential distribution over 2 orders of magnitude in concentration; (ii...

NM-landscapes have been recently introduced as a class of tunable rugged models. They are a subset of the general interaction models where all the interactions are of order less or equal M . The Boltzmann distribution has been extensively applied in single-objective evolutionary algorithms to implement selection and study the theoretical properties of model-building algorithms. In this paper we...

In this paper, by introducing a different distribution function and starting from the Boltzmann equation as well as the Maxwell-Boltzmann distribution, we obtain a Boltzmann Bhatnagar-Gross-Krook (BGK) equation for thermal flows with viscous heat dissipation in the incompressible limit. The continuous thermal BGK model is then discretized over both time and phase space to form a lattice BGK mod...

The Boltzmann–Gibbs distribution is currently widely used in economic modeling. One of the applications is integrated with the DSGE (Dynamic Stochastic General Equilibrium) model. However, a question that arises concerns whether the Boltzmann–Gibbs distribution can be directly applied, without considering the underlying social network structure more seriously, even though the social network str...

While DSGE models have been widely used by central banks for policy analysis, they seem to have been ineffective in calibrating the models for anticipating financial crises. To bring DSGE models closer to real situations, some of researchers have revised the traditional DSGE models. One of the modified DSGE models is the adaptive belief system model. In this framework, changes in sentiment can ...

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to – justified or not – hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann) we demonstrate how the corresponding entropy has to look like, given the form of the corresponding distribution functions. By two natural assumptions that (i) t...

We prove that the Boltzmann-Grad limit of the Lorentz gas with periodic distribution of scatterers cannot be described with a linear Boltzmann equation. This is at variance with the case of a Poisson distribution of scatterers, for which the convergence to the linear Boltzmann equation was proved by Gallavotti [Phys. Rev. (2) 185, 308 (1969)]. The arguments presented here complete the analysis ...