Related papers: Dynamical approach to the microcanonical ensemble
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…
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…
In the general case of a many-body Hamiltonian system, described by an autonomous Hamiltonian $H$, and with $K\geq 0$ independent conserved quantities, we derive the microcanonical thermodynamics. By a simple approach, based on the…
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…
Two approaches to describe the thermodynamics of a subsystem that interacts with a thermal bath are considered. Within the first approach, the mean system energy $E_{S}$ is identified with the expectation value of the system Hamiltonian,…
Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
In traditional thermodynamical and statistical-mechanical approaches one has (some) detailed knowledge of the principles governing the microdynamics of a system. However in many instances we may not have a Hamiltonian or good information…
We propose statistical systems based on $p$-adic numbers. In the systems, the Hamiltonian is a standard real number which is given by a map from the $p$-adic numbers. Therefore we can introduce the temperature as a real number and calculate…
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
We investigate a one-dimenisonal Hamiltonian system that describes a system of particles interacting through short-range repulsive potentials. Depending on the particle mean energy, $\epsilon$, the system demonstrates a spectrum of kinetic…
The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
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…
This work is an attempt to give a brief overview of the implementation of the statistical ther- modynamics to hadronic matter. The possibility to use the hydrodynamic approach for developing the physical model of the formation of exotic…
We construct an effective low-energy Hamiltonian from the classical action via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute matrix elements of the transition amplitude and (ii) to construct stochastically a basis.…
We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the co-evolving charged particles. The equilibrium statistical mechanics solution of the model is worked out…