Related papers: Mixing and irreversibility in classical mechanics
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…
Hybrid molecular dynamics/Monte Carlo simulations used to study melts of unentangled, thermoreversibly associating supramolecular polymers. In this first of a series of papers, we describe and validate a model that is effective in…
We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The microscopic deterministic mechanism of the irreversible equilibration process in…
The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
A recent proposal for mixed dynamics of classical and quantum ensembles is shown, in contrast to other proposals, to satisfy the minimal algebraic requirements proposed by Salcedo for any consistent formulation of such dynamics. Generalised…
The mixing of two different gases is one of the most common natural phenomena, with applications ranging from CO$_2$ capture to water purification. Traditionally, mixing is analyzed in the context of local thermal equilibrium, where systems…
The literature on dynamical systems has, for the most part, considered self-oscillators (i.e., systems capable of generating and maintaining a periodic motion at the expense of an external energy source with no corresponding periodicity)…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
This article aims at revisiting, with the aid of simple and neat numerical examples, some of the basic features of macroscopic irreversibility, and, thus, of the mechanical foundation of the second principle of thermodynamics as drawn by…
Master equation could be applied to model various kinds of biochemical systems. A general theory for its time-dependent nonequilibrium thermodynamics is rigorously derived. We not only introduce a concept of general internal energy, but…
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…
In many far-from-equilibrium biological systems, energy injected by irreversible processes at microscopic scales propagates to larger scales to fulfill important biological functions. But given dissipative dynamics at the microscale, how…
The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a…
The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small…
Identifying dissipation is essential for understanding the physical mechanisms underlying nonequilibrium processes. {In living systems, for example, the dissipation is directly related to the hydrolysis of fuel molecules such as adenosine…
In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems…