Related papers: Microcanonical phase transitions in small systems
The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying…
We present an exact microcanonical formulation, in the thermodynamic limit, for a system of $N$ noninteracting particles with $p$ equally spaced energy levels $\{0,\epsilon,2\epsilon,\ldots,(p-1)\epsilon\}$. Writing the microcanonical…
The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the…
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard…
The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in…
In the general case of a many-body Hamiltonian system, described by an autonomous Hamiltonian $H$, and with $K\geq 0$ independent conserved quantities, we derive the microcanonical thermodynamics. By a simple approach, based on the…
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…
Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic…
Traditionally, phase transitions are defined in the thermodynamic limit only. We propose a new formulation of equilibrium thermo-dynamics that is based entirely on mechanics and reflects just the {\em geometry and topology} of the N-body…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
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…
Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including…
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,…
For a closed bi-partite quantum system partitioned into system proper and environment we interprete the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible…
We study a generalized isotropic XY-model which includes both two-spin and four-spin mean-field interactions. This model can be solved in the microcanonical ensemble. It is shown that in certain parameter regions the model exhibits gaps in…
Nonanalyticities of thermodynamic functions are studied by adopting an approach based on stationary points of the potential energy. For finite systems, each stationary point is found to cause a nonanalyticity in the microcanonical entropy,…
We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact…
Phase transitions are one of the most interesting natural phenomena. For finite systems, one of the concerns in the topic is how to classify a specific transition as being of first, second, or even of a higher order, according to the…