We present critical arguments against individual interpretation of Bohr’s complementarity and Heisenberg’s uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the possibility to use Statistical Contextual Realist Interpretation of quantum formalism. In spite of all no-go theorems (e.g., von Neumann, Kochen and Specker,..., ...

We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and Susskind to constructions of stochastic processes related to quantum statistical mechanical systems on Cuntz– Krieger algebras. We extend the eternal inflation model from the Bruhat–Tits tree to quotients by p-adic Schottky groups, again using quantum statistical mechanics on graph algebras.

Noting that quantum measurements are in general incomplete, we develop, starting from a recent entropic formulation of uncertainty, a mazimum uncertainty principle to define the statistical mechanics of microscopic systems. The resulting ensemble entropy coincides with the expression of von Neumann, thus providing a unified, quantum basis for statistical physics of all systems. Examples involvi...

We present a theory where the statistical mechanics for dilute ideal gases can be derived from random matrix approach. We show the connection of this approach with Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory, thus providing a unified edifice for quantum chaos, random matrix theory an...

Several studies in quantum mechanics and statistical mechanics have formally established that nonflat metrics induce a difference in the potential used to define the path-integral Lagrangian from that used to define the differential Schr̈odinger Hamiltonian. A recent study has described a statistical mechanical biophysical system in which this effect is large enough to be measurable. This study ...

I give a simple proof that the correlation functions of many-fermion systems have a convergent functional Grassmann integral representation, and use this representation to show that the cumulants of fermionic quantum statistical mechanics satisfy l–clustering estimates.

In ordinary nonrelativistic quantum mechanics (QM), the observables pertaining to a system typically form the self-adjoint part of the algebra B(H) of bounded operators acting on a Hilbert space H.1 B(H) is an algebra of the genus von Neumann and the species Type I factor.2 Here we consider quantum systems whose observable-algebras belong to the same genus, but correspond to more exotic species...

The method of positive commutators, developed for zero temperature problems over the last twenty years, has been powering progress in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an alternative proof of a fundamental property of l...