Related papers: Extremum complexity in the monodimensional ideal g…
The probability distribution for vacuum fluctuations of the energy flux in two dimensions will be constructed, along with the joint distribution of energy flux and energy density. Our approach will be based on previous work on probability…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
We study a one-dimensional model for granular gases, the so-called Inelastic Maxwell Model. We show theoretically the existence of stationary solutions of the unforced case, that are characterized by an infinite average energy per particle.…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
We study a one-dimensional gas of $n$ charged particles confined by a potential and interacting through the Riesz potential or a more general potential. In equilibrium, and for symmetric potential the particles arrange themselves…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
A theory is developed for the evolution of the non-equilibrium distribution of quasiparticles when the scattering rate decreases due to particle collisions. We propose a "modified one-collision approximation" which is most effective for…
The quasi-stationary nonequilibrium distribution function of an independent electron gas interacting with a medium, which is at local thermal equilibrium, can be obtained by entropy production rate minimization, subject to constraints of…
In weakly collisional stellar systems such as some globular clusters, partial energy equipartition and mass segregation are expected to develop as a result of the cumulative effect of stellar encounters even in systems initially…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…
The mutual derivation between arbitrary distribution forms of momenta and momentum components of particles produced in an isotropic emission source are systematically studied in terms of probability theory and mathematical statistics. The…
The dynamics of individual colloidal particles in random potential energy landscapes were investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a…
We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the…
We study the deterministic dynamics of non-interacting classical gas particles confined to a one-dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone…
At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic…
We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when…