Related papers: Geometric Microcanonical Thermodynamics for System…
We consider a generic classical many particle system described by an autonomous Hamiltonian $H(x^{_1},...,x^{_{N+2}})$ which, in addition, has a conserved quantity $V(x^{_1},...,x^{_{N+2}})=v$, so that the Poisson bracket $\{H,V \}$…
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…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
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…
We consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law…
We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the micro canonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a…
It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we…
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…
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…
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…
Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical…
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…
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal…
The state of a thermodynamic system being characterized by its set of extensive variables $q^{i}(i=1,...,n) ,$ we write the associated intensive variables $\gamma_{i},$ the partial derivatives of the entropy $ S(q^{1},...,q^{n}) \equiv…
The Variation After Projection approach is applied for the first time to the pairing hamiltonian to describe the thermodynamics of small systems with fixed particle number. The minimization of the free energy is made by a direct…
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…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…
We present a universal thermodynamic framework for quantum systems that may be strongly coupled to thermal environments. Unlike previous approaches, our method enables a clear definition of thermostatic properties while preserving the same…
We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian…