Related papers: Covariant Equilibrium Statistical Mechanics
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
The fundamental concept of phase space for particles moving in the four-dimensional spacetime is analyzed. Particle distribution density is defined as differential form, which degree may be different in various cases. It should be…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing…
Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical…
The method of constructing of extended phase space for singular theories which permits the consideration of covariant gauges without the introducing of a ghost fields, is proposed. The extension of the phase space is carried out by the…
Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical evolution of the leaf volume along local unstable manifolds.…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
The theories known as doubly special relativity are introduced in order to take into account an observer-independent length scale and the speed of light in the framework of special relativity. These theories can be generally formulated on…
New exact completely closed homogeneous Generalized Master Equations (GMEs), governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of s particles (s<N) selected from N>>1…
The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element.…
It is proved in the paper that the non-conservative dissipative force and asymmetry of time reversal can be naturally introduced into classical statistical mechanics after retarded electromagnetic interaction between charged microparticles…
A gauge-invariant wave equation for the dynamics of hybrid quantum-classical systems is formulated by combining the variational setting of Lagrangian paths in continuum theories with Koopman wavefunctions in classical mechanics. We identify…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by…
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
Previously developed ``stochastic representation of deterministic interactions`` enables exact treatment of an open system without leaving its native phase space (Hilbert space) due to peculiar stochastic extension of the Liouville (von…