Related papers: Dynamical approach to the microcanonical ensemble
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…
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…
The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…
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 dynamics of short 1D nonlinear Hamiltonian chains is analyzed numerically at different temperatures (energy per particle). The boundary temperature $T_b$ separating the regular (quasiperiodic) and the stochastic (chaotic) chain motion…
The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
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…
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of…
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 Hamiltonian dynamics is defined for the XY model by adding a kinetic energy term. Thermodynamical properties (total energy, magnetization, vorticity) derived from microcanonical simulations of this model are found to be in agreement with…
We consider a small Hamiltonian system strongly interacting with a much larger Hamiltonian system (the bath), while being driven by both a time-dependent control parameter and non-conservative forces. The joint system is assumed to be…
A universal algorithm to derive a macroscopic dynamics from the microscopic dynamical system via the averaging process and symplecto-contact reduction was introduced by Jin-wook Lim and the second-named author in [LO23]. They apply the…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. However, its original formulation is not, in general, thermodynamically consistent,…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…