The study of strongly out-of-equilibrium states and their time evolution towards thermalization is critical to the understanding an ever widening range physical processes. We present a numerical method that for first allows solution most difficult part time-dependent Boltzmann equation: full scattering term. Any number bands (and quasiparticles) with arbitrary dispersion, any high order channel...

One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+{\rm div}(D(x)b(u)u)=0, t\geq0, x\in\mathbb{R}^d,\qquad (1)$$ and under appropriate hypotheses on $\beta,$ $D$ $b$ convergence in $L^1_\textrm{loc}(\mathbb{R}^d)$, $L^1(\mathbb{R}^d)$, respectively, some $t_n\to\infty$ of solution $u(t_n)$ an equilibrium state large set nonn...

We present a generalization of the Density Functional Theory to distributions in μ-space rather than in configuration space. This equilibrium theory is the basic ingredient for constructing a dynamic theory with projection operators. The reversible part of the dynamics is computed exactly while the irreversible part is approximated with a fast momentum relaxation assumption. As a result the irr...

Abstract. We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group providing a unique deterministic description of irreversible, conservative relaxation towards equilibrium from any non-equilibrium state, and satisfies ...

We present a method for constructing equilibrium disks with net angular momentum in general relativity. The method solves the relativistic Vlasov equation coupled to Einstein’s equations for the gravitational field. We apply the method to construct disks that are relativistic versions of Newtonian Kalnajs disks. In Newtonian gravity these disks are analytic, and are stable against ring formatio...