Related papers: Non-Equilibrium Statistical Mechanics of Classical…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to…
In this note we describe some results concerning non-relativistic quantum systems at positive temperature and density confined to macroscopically large regions of physical space which are under the influence of some local, time-dependent…
The quantum master equation obtained by generalizing the geometric formulation of nonequilibrium thermodynamics to dissipative quantum systems is seriously nonlinear. We argue that nonlinearity occurs naturally in the step from reversible…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble, whereas canonical ones fail in the most interesting, mostly inhomogeneous, situations like phase separations or away from the thermodynamic…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…
The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of harmonic oscillators…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…