Related papers: Direct derivation of microcanonical ensemble avera…
Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical…
Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative…
Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical…
In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the standard mode…
We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and…
So-called average subsystem entropies are defined by first taking partial traces over some pure state to define density matrices, then calculating the subsystem entropies, and finally averaging over the pure states to define the average…
The characterization of physical systems relies on the observable properties which are measured, and how such measurements are performed. Here we analyze two ways of assigning a description to a quantum system assuming that we only have…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…
The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the…
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
We investigate the time evolution of a generic and finite isolated quantum many-body system starting from a pure quantum state. We find the kinematical general canonical principle proposed by Popescu-Short-Winter for statistical mechanics…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
We consider the generalization of a matrix integral with arbitrary spectral curve $\rho_0(E)$ to a 0+1D theory of matrix quantum mechanics (MQM). Using recent techniques for 1D quantum systems at large-$N$, we formulate a hydrodynamical…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions…
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…
The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution…
Calculating thermodynamic potentials and observables efficiently and accurately is key for the application of statistical mechanics simulations to materials science. However, naive Monte Carlo approaches, on which such calculations are…
A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of…