Related papers: Hierarchy of space-time structures, Boltzmann equa…
The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics. This problem was considered by Boltzmann, Poincar\'e, Bogolyubov and many other authors and though some…
A derivation of the Boltzmann equation from the Liouville equation by the use of the Grad limiting procedure in a finite volume is proposed. We introduce two scales of space-time: macro- and microscale and use the BBGKY hierarchy and the…
Time reversal symmetry is a fundamental property of many quantum mechanical systems. The relation between statistical physics and time reversal is subtle and not all statistical theories conserve this particular symmetry, most notably…
It is a remarkable fact that all processes occurring in the observable Universe are irreversible, whereas the equations through which the fundamental laws of physics are formulated are invariant under time reversal. The emergence of…
An attempt is made to de-mystify the apparent "paradox" between microscopic time revsersibility and macroscopic time irreversibility. It is our common experience that a hot cup of coffee cools down to room temperature and it never…
The issue of how time reversible microscopic dynamics gives rise to macroscopic irreversible processes has been a recurrent issue in Physics since the time of Boltzmann whose ideas shaped, and essentially resolved, such an apparent…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
We consider the microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov. The fact that the time-irreversible kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox…
It is shown that early suggested derivation of the Boltzmann kinetic equation for dilute hard sphere gas from the time-reversible BBGKY equations is incorrect since in fact a priori substitutes for them definite irreversible equations.…
The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last…
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
In the second half of the 19th century, the kinetic theory of gases has probably raised one of the most impassioned debates in the history of science. The so-called reversibility paradox around which intense polemics occurred reveals the…
Time-reversal had always been assumed to be a symmetry of physics at the fundamental level. In this paper we will explore the violations of time-reversal symmetry at the fundamental level and the consequences on thermodynamic systems.…
Time reversal symmetry is a fundamental property of many quantum mechanical systems. The relation between statistical physics and time reversal is subtle and not all statistical theories conserve this particular symmetry, most notably…
All of the basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system…
Based on an extended time-space symmetry, a cylindrical model of gravitational geometrical dynamics with two time-like extra-dimensions leads to a microscopic geodesic description of the curved space-time. Due to interaction of a Higgs-like…
It is a remarkable fact that all processes occurring in the observable Universe are irreversible, whereas the equations in which the laws of physics are formulated are invariant under time reversal. The emergency of irreversibility from the…
A generalization of the Gibbs-von Neumann relative entropy is proposed based on the quantum BBGKY [Bogolyubov-Born-Green-Kirkwood-Yvon] hierarchy as the nonequilibrium entropy for an N-body system. By using a generalization of the…
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations of motion are time reversal invariant. One objection to irreversibility is based on Poincar\'e's recursion theorem: a…