Related papers: Subdynamics of a many-particle classical system dr…
The transport behavior of a system of gravitationally driven colloidal particles is investigated. The particle interactions are determined by the superparamagnetic behavior of the particles. They can thus be arranged in a crystalline order…
By examining both the divergence of the velocity vector in orthogonal Cartesian coordinate space $\mathbf{\Gamma} $ of dimension $\R^{\textrm {2fN}}$ and the structure of the Hamiltonian determining a system trajectory, it is shown that the…
A generalization of the Gibbs entropy postulate is proposed based on the BBGKY hierarchy as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…
The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of…
By generalizing Bogolyubov's reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained…
We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component $\phi_j$ of the wave vector is understood as a…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
It was recently shown that Newtonian dynamics of macroscopic particles can be derived from unitary Schr\"odinger evolution under an assumption on the system-environment interaction, namely that the interaction Hamiltonian effectively…
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…
In this paper we presented an overview on our works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type's…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
Active suspensions composed of self-propelled colloidal particles are considered. Their propulsion of is generated by chemical reactions occurring by heterogeneous catalysis and diffusiophoresis coupling the concentration gradients of…
A theoretical description of quantum mechanical steady states is developed. Applications for simple quantum mechanical systems described in terms of coupled level structures yield a formulation equivalent to time independent scattering…
We investigate a novel type of Langevin model that describes the nonequilibrium dynamics of a classical particle interacting with a spatially extended environment. In this model, a particle, which interacts with the environment through the…
From Liouville's equation, a phase-space multi-scale transport equation is systematically derived. The proposed phase-space multi-scale transport equation based on the first principle indicates that the nonlinear stochastic transport is due…
Although the overwhelming majority of natural processes occurs far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introducing description of open dissipative…
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…