Related papers: Pathological limits in statistical mechanics
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to physically realizable examples…
A survey of the approach to Statistical Mechanics following Boltzmann's theory of ensembles and ergodic hypothesis leading to chaoticity as a unifying principle of equilibrium and nonequilibrium Statistical Mechanics.
An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. Excluded volume effects are taken into account in the thermodynamically self-consistent way. The model exhibits a 1-st order phase…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…
A view on the physical meaning of the so called ergodic hypothesis: its role on the foundations of equilibrium statistical mechanics in mid '800, its interpretations and hints at its relevance for modern nonequilibrium statistical…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc) of the asymptotic laws and of convergence rates were studied. However, for basically all…
We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. This approach has the advantage that statistical mechanics is much better…
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
The recent argue about the existence of an instability in the definition of the mean value appearing in the Tsallis non extensive Statistical Mechanic is reconsidered. Here, it is simply underlined that the pair of probability distributions…
Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…