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The theoretical cornerstone of statistical mechanics is the ergodic assumption that all accessible configurations of a physical system are equally likely. Here we show how such property arises when an open quantum system is continuously…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they…
Effects of quantum statistics for nuclear matter equation of state are analyzed in terms of the recently proposed quantum van der Waals model. The system pressure is expanded over a small parameter $\delta \propto…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
We apply the atom counting theory to strongly correlated Fermi systems and spin models, which can be realized with ultracold atoms. The counting distributions are typically sub-Poissonian and remain smooth at quantum phase transitions, but…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit - when the number of particles becomes very large. Here, we study thermodynamics in the opposite regime - at both the nano scale, and when…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…