Related papers: Ensemble equivalence for general many-body systems
We study the Hamiltonian Mean Field (HMF) model, a system of $N$ fully coupled particles, in the microcanonical ensemble. We use the previously obtained free energy in the canonical ensemble to derive entropy as a function of energy, using…
The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable…
It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by…
The microcanonical entropy s(e,m) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie-Weiss-type interactions. The result shows a number of interesting…
Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulae for the microcanonical partition functions in the case of non-interacting massless neutral particles…
We addressed the problem of generalizing the extensive postulates of the standard thermodynamics in order to extend it to the study of nonextensive systems. We did it in analogy with the traditional analysis, starting from the…
A recent description of an exact map for the equilibrium structure and thermodynamics of a quantum system onto a corresponding classical system is summarized. Approximate implementations are constructed by pinning exact limits (ideal gas,…
We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble the system i) obeys a barometric formula for the density profile and ii) the kinetic…
Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…
Preparing thermal equilibrium states is an essential task for finite-temperature quantum simulations. In statistical mechanics, microstates in thermal equilibrium can be obtained from statistical ensembles. To date, numerous ensembles have…
We reconsider the Boltzmann-Gibbs statistical ensemble in thermodynamics using the multinomial coefficient approach. We show that an ensemble is defined by the determination of four statistical quantities, the element probabilities $p_i$,…
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…
We consider a system of globally coupled rotors, described by a set of Langevin equations, and examine stability of the incoherent phase. The corresponding Fokker-Planck equation, providing a unified description of microcanonical and…
Designing the phase behavior of multicomponent mixtures is a rich area with many potential applications. One key question is how more than $M+1$ phases, as would normally be allowed by Gibbs' phase rule at generic temperature in a mixture…
A multicanonical formalism is applied to the problem of statistical equilibrium in a complex system with a hierarchy of dynamical structures. At the small scales the system is in quasi-equilibrium and follows a Maxwell-Boltzmann…
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…
We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the…
Multi-agent complex systems comprising populations of decision-making particles, have wide application across the biological, informational and social sciences. We uncover a formal analogy between these systems' time-averaged dynamics and…
The aim of this paper is to use large deviation theory in order to compute the entropy of macrostates for the microcanonical measure of the shallow water system. The main prediction of this full statistical mechanics computation is the…