I review the role of probability in contemporary physics and the origin of probabilistic time asymmetry, beginning with the pre-quantum case (both stochastic mechanics and classical statistical mechanics) but concentrating on quantum theory. I argue that quantum mechanics radically changes the pre-quantum situation and that the philosophical nature of objective probability in physics, and of pr...

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 variables. The quantum contribution is given by the term of the second order. To escape technical difficulties related to the infinite dimension of phase space f...

We attempt a unification of the Quantum and the Statistical Mechanics of a single spinless particle. We consider a five dimensional (5D) space-time with no matter. We postulate that all the physical information on a 5D massless particle propagation is provided by the statistics over null paths in this 5D space-time. If the 5D metric does not depend on the fifth space-like coordinate, then the p...

Much of the evidence for quantum mechanics is statistical in nature. The Everett interpretation, if it is to be a candidate for serious consideration, must be capable of doing justice to reasoning on which statistical evidence in which observed relative frequencies that closely match calculated probabilities counts as evidence in favour of a theory from which the probabilities are calculated. S...

This work presents a comparison of Quantum and Statistical Mechanics at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, an...

This work presents a comparison of Quantum and Statistical Mechanics at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, an...

We describe recent progress towards deriving the Fundamental Laws of thermodynamics (the 0, 1, and 2 Law) from nonequilibrium quantum statistical mechanics in simple, yet physically relevant models. Along the way, we clarify some basic thermodynamic notions and discuss various reversible and irreversible thermodynamic processes from the point of view of quantum statistical mechanics.

We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in [JP4, JP5, JP6, Ru3, Ru4, Ru5, Ru6]. In the algebraic formalism of quantum statistical mechanics we introduce notions of non-equilibrium steady states, entropy production and heat fluxes, and study their properties. Our basic paradigm is a model of a small (finite) quant...