Related papers: Simple spin models with non-concave entropies
We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger spin ensemble of any geometry with…
Microcanonical equations for several thermodynamic properties of a system, suitable for molecular dynamics simulations, are derived from the nonextensive Tsallis entropy functional. Two possible definitions of temperature, the usual one and…
Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be…
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…
Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called…
Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical…
We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual…
The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying…
For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged…
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian, and the calculation of…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that…
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,…
A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular…
A well-established numerical technique to study the dynamics of spin systems in which symmetries and conservation laws play an important role is to microcanonically integrate their reversible equations of motion, obtaining thermalization…
Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here we propose a theory of…
In this micro-canonical simulation the temperature and also the specific heat are determined as averages of expressions easy to implement. The XY-chain is studied for a test. The second order transition on a cubic lattice and the first…
We show that entropy is globally concave with respect to energy for a rich class of mean field interactions, including regularizations of the the point-vortex model in the plane, plasmas and self-gravitating matter in 2D, as well as the…
The statistical properties of non-interacting bosons and fermions confined in trapping potentials are most easily obtained when the system may exchange energy and particles with a large reservoir (grand-canonical ensemble). There are…
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…