Related papers: Pathological limits in statistical mechanics
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…
Analysis of experimental data must sometimes deal with abrupt changes in the distribution of measured values. Setting upper limits on signals usually involves a veto procedure that excludes data not described by an assumed statistical…
The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the…
It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of…
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this…
A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific…
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…
We briefly review the present status of nonextensive statistical mechanics. We focus on (i) the central equations of the formalism, (ii) the most recent applications in physics and other sciences, (iii) the {\it a priori} determination…
Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
The quantum mechanical bound states of the $-{\alpha}/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the…
A novel way of defining limits in classical statistics is proposed. This is a natural extension of the original Neyman's method, and has the desirable property that only information relevant to the problem is used in making statistical…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon's interests. In particular, we focus on rigorous non-perturbative results…
Statistics experiences a storm around the perceived misuse and possible abuse of its methods in the context of the so-called reproducibility crisis. The methods and styles of quantification practiced in mathematical modelling rarely make it…
During the past few years, nonextensive statistics has been successfully applied to explain many different kinds of systems. Through these studies some interpretations of the entropic parameter q, which has major role in this statistics, in…