Related papers: Application of classical statistical mechanics to …
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a…
The relationships between reversible Carnot cycles, the absence of perpetual motion machines and the existence of a non-decreasing, globally unique entropy function forms the starting point of many textbook presentations of the foundations…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
This is the fourth paper, the last one, on solution to the problem of absence of detailed balance in nonequilibrium processes. It is an approach based on another known universal dynamics: The evolutionary dynamics first conceived by Darwin…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E49, 5103 (1994)] as a…
Time dynamics of isolated many-body quantum systems has long been an elusive subject. Very recently, however, meaningful experimental studies of the problem have finally become possible, stimulating theoretical interest as well. Progress in…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system…
We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…
We develop a finite temperature field theory formalism in any dimension that has the filling fractions as the basic dynamical variables. The formalism efficiently decouples zero temperature dynamics from the quantum statistical sums. The…
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of…
Obtaining accurate field statistics continues to be one of the major challenges in turbulence theory and modeling. From the various existing modeling approaches, multifractal models have been successful in capturing intermittency in…
The purpose of this paper is two-fold. First, to make clear (and de-mystify) the basic concepts of classical thermodynamics, and thus to enable the integration of thermodynamics within systems modeling and control. Second, to demonstrate…
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…
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…