Related papers: Strange Lagrangian systems and statistical mechani…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
The mean-field thermodynamic limit is studied for a class of isolated Newtonian N-body systems whose Hamiltonian admits several invariants of motion. It is shown that the macrostates of individual members of a statistical equilibrium…
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…
For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation relations with the evolution operators of Lagrangian and Hamiltonian formalisms. Separate…
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories,…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
We adopt a 'thermodynamical' formulation of Mach's principle that the rest mass of a particle in the Universe is a measure of its long-range collective interactions with all other particles inside the horizon. We consider all particles in…
For the system with inhomogeneous distribution of macroscopic parameters we obtain thermodynamic relation which depends on the spatial point (coordinate). In our approach, to obtain such a relation we use the basic ideas of the method of…
This work deals with the physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential in the context of…
We show that when the thermal wavelength is comparable to the spatial size of a system, thermodynamic observables like Pressure and Volume have quantum fluctuations that cannot be ignored. They are now represented by operators; conventional…
We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann's principle,…
A thermodynamic model for multifragmentation which is frequently used appears to give very different values for specific heat at constant volume depending upon whether canonical or grand canonical ensemble is used. The cause for this…