Related papers: Simple spin models with non-concave entropies
Entropy is critically examined as a fundamental concept in contemporary science and informatics. Although the typical Shannon entropy provides a proper framework for describing the canonical ensemble, it fails to represent adequately the…
Two formulations of relativistic hydrodynamics of particles with spin 1/2 are compared. The first approach, dubbed the canonical one, uses expressions for the energy-momentum and spin tensors that have properties that follow a direct…
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…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
We study the configurational probability distribution of a mono-atomic gas with a finite number of particles N in the micro-canonical ensemble. We give two arguments why the thermodynamic entropy of the configurational subsystem involves…
We apply the method of gauge transformation to spin glasses under the microcanonical ensemble to study the possibility of ensemble inequivalence in systems with long-range interactions and quenched disorder. It is proved that all the…
We analyze a microscopic decoherence model in which the total system is described as a spin gas. A spin gas consists of N classically moving particles with additional, interacting quantum degrees of freedom (e.g. spins). For various…
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…
I shortly describe semi-classical models of spinning electron and list a number of theoretical issues where these models turn out to be useful, see arXiv:1710.07135 for details. Then I discuss the possibility to extend the range of…
We study equilibrium states of quantum spin systems with non-additive long-range interactions by adopting an appropriate scaling of the interaction strength, i.e., the so called Kac prescription. In classical spin systems, it is known that…
A variety of quantum gravity models (including spin foams) can be described using a path integral formulation. A path integral has a well-known statistical mechanical interpretation in connection with a canonical ensemble. In this sense, a…
We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
In this work, the zero-temperature limit of the thermodynamic spin-density functional theory is investigated. The coarse-grained approach to the equilibrium density operator is used to describe the equilibrium state. The characteristic…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
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…
Spin-echo experiments are often said to constitute an instant of anti-thermodynamic behavior in a concrete physical system that violates the second law of thermodynamics. We argue that a proper thermodynamic treatment of the effect should…
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 limit free energy of spin-glass models with convex interactions can be represented as a variational problem involving an explicit functional. Models with non-convex interactions are much less well-understood, and simple variational…
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from…