Related papers: Remarks about the Phase Transitions within the Mic…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
Microcanonical statistics can be well applied to non-extensive systems like nuclei, atomic clusters and systems at phase transitions of first order with inhomogeneous configurations like phase separation. No thermodynamic limit has to be…
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…
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
When studying the thermodynamic properties of mesoscopic systems the most appropriate microcanonical entropy is the volume entropy, i.e. the logarithm of the volume of phase space enclosed by the hypersurface of constant energy. For systems…
The microcanonical ensemble is in important physical situations different from the canonical one even in the thermodynamic limit. In contrast to the canonical ensemble it does not suppress spatially inhomogeneous configurations like phase…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
Microcanonical thermodynamics (MCTh) is contrasted to canonical thermodynamics (CTh). At phase transitions of 1.order the two ensembles are NOT equivalent even in the thermodynamic limit . Energy fluctuations do not vanish and phase…
We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of second kind, i.e. for which the equivalence of…
The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…
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…
Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the canonical formulation, carry important information…
Microcanonical thermodynamics (MT) is analysed for phase transitions of first and second order in finite systems. The transiton temperature, the latent heat and the surface tension of first order transitions can easily be determined by MT…
A microcanonical first order transition, connecting a clustered to a homogeneous phase, is studied from both the thermodynamic and dynamical point of view for a N-body Hamiltonian system with infinite-range couplings. In the microcanonical…
This paper reviews a number of fundamental connections that exist between nonequivalent microcanonical and canonical ensembles, the appearance of first-order phase transitions in the canonical ensemble, and thermodynamic metastable…
We present data indicating that the recent evidence for the phase transition being of first order does not result from a breakdown of the ergodicity of the algorithm. We also present data showing that the thermodynamical limit of the model…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
We study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at precisely the energy density associated with the dynamical…