Related papers: Nonequilibrium representative ensembles for isolat…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
The quasi-static evolution of steady states far from equilibrium is investigated from the point of view of quantum statistical mechanics. As a concrete example of a thermodynamic system, a two-level quantum dot coupled to several reservoirs…
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…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Determining the role of initial conditions in the late time evolution is a key issue for the theory of nonequilibrium dynamics of isolated quantum systems. Here we extend the theory of quantum quenches to the case in which before the quench…
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide…
It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a…
The dynamics of quantum entanglement plays a central role in explaining the emergence of thermal equilibrium in isolated many-body systems. However, entanglement is notoriously hard to measure. Recent works have introduced a notion of…
The mean-field thermodynamic limit is studied for a class of isolated Newtonian N-body systems whose Hamiltonian admits several invariants of motion. It is shown that the macrostates of individual members of a statistical equilibrium…
We investigate the correspondence between a non-equilibrium ensemble defined via the distribution of phase-space paths of a Hamiltonian system, and a system driven into a steady-state by non-equilibrium boundary conditions. To discover…
The integrable system is constrained strictly by the conservation law during the time evolution, and the nearly integrable system or nonintegrable system is also constrained by the conserved parameters (like the constants of motion) with…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
The internal energy of individual subsystems is not well defined in interacting quantum systems, leading to ambiguities in the definition of thermodynamic quantities. Applying the Schmidt basis formalism to general bipartite autonomous…
The main purpose of this tutorial is to elucidate in details what should be meant by ensemble of states in quantum mechanics, and to properly address the problem of discriminating, exactly or approximately, two different ensembles. To this…
The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed, provided all these superpositions have the same fixed energy.…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…