Related papers: The Multifractal Time and Irreversibility in Dynam…
The approach to the analysis of the dynamic of non-equilibrium open systems within the framework of the laws of classical mechanics on the example a hard-disks is offered. This approach was based on Hamilton and Liouville generalized…
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…
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to…
In this paper, the emergence of macroscopic-scale pseudo time-irreversibility is studied in the closed classical many-body system of pair interacting particles. First, exact continuum equations are derived to the Hamiltonian dynamics…
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and…
The irreversible turbulent energy cascade epitomizes strongly non-equilibrium systems. At the level of single fluid particles, time irreversibility is revealed by the asymmetry of the rate of kinetic energy change, the Lagrangian power,…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
The mechanism of irreversible dynamics in the mixing systems is constructed in the frames of the classical mechanics laws. The offered mechanism can be found only within the framework of the generalized Hamilton's formalism. The generalized…
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…
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…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
What forms will have an equations of modern physics if the dimensions of our time and space are fractional? The generalized equations enumerated by title are presented by help the generalized fractional derivatives of Riemann-Liouville.
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…
Understanding irreversibility in macrophysics from reversible microphysics has been the holy grail in statistical physics ever since the mid-19th century. Here the central question concerns the arrow of time, which boils down to deriving…
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
An equation describing the irreversible evolution of the local density of a continuous medium without involving any statistical hypotheses and assumptions is derived. The derivation is based on the smoothing of the microscopic dynamic…
The fluctuation relations, which characterize irreversible processes in Nature, are among the most important results in non-equilibrium physics. In short, these relations say that it is exponentially unlikely for us to observe a…