Related papers: Microcanonical analysis of small systems
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy…
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…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived, and are used to establish the existence of phase transitions…
In the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions. In this approach the quantities of interest are exclusively expressed as derivatives of the…
Microcanonical analysis is a powerful method for studying phase transitions of finite-size systems. This method has been used so far only for studying phase transitions of equilibrium systems, which can be described by microcanonical…
We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on…
In the microcanonical ensemble, suitably defined observables show non-analyticities and power law behaviour even for finite systems. For these observables, a microcanonical finite-size scaling theory is established which facilitates an…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
The most complicated phenomena of equilibrium statistics, phase separations and transitions of various order and critical phenomena, can clearly and sharply be seen even for small systems in the topology of the curvature of the…
A microcanonical finite-size scaling ansatz is discussed. It exploits the existence of a well-defined transition point for systems of finite size in the microcanonical ensemble. The best data collapse obtained for small systems yields…
By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of…
Conventional thermo-statistics address infinite homogeneous systems within the canonical ensemble. However, some 150 years ago the original motivation of thermodynamics was the description of steam engines, i.e. boiling water. Its essential…
Physical quantities obtained from the microcanonical entropy surfaces of classical spin systems show typical features of phase transitions already in finite systems. It is demonstrated that the singular behaviour of the microcanonically…
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 continuous ferromagnetic-paramagnetic phase transition in the two-dimensional Ising model has already been excessively studied by conventional canonical statistical analysis in the past. We use the recently developed generalized…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
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…
Phase transitions are conventionally defined by nonanalyticities of thermodynamic potentials in the thermodynamic limit. In this Letter, we show that the singularity is not the definition of criticality but its asymptotic outcome:…
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…