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Classical Statistical Mechanics
2003Some aspects of statistical mechanics that are particularly important for computer simulation approaches are recalled. Using Ising and classical Heisenberg models as examples, various statistical ensembles and appropriate thermodynamic potentials are introduced, and concepts such as Legendre transformations between ensembles and the thermodynamic ...
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Classical Statistical Mechanics
2015According to classical mechanics, equations of motion supplemented by initial conditions uniquely determine the subsequent evolution of a given system. For typical systems of our interest, however, the number of mechanical degrees of freedom is of the order of 1024. One cannot possibly write down 1024 equations of motion, much less solve them.
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Statistical mechanics of classical systems
Soviet Physics Journal, 1980An algebra of thermodynamic operators of the fluctuations of physical quantities in classical statistical mechanics is found and its properties studied. A method is proposed for obtaining equations that describe the equilibrium and nonequilibrium statistical ensembles of classical systems.
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Statistical methods in classical mechanics
Reports on Mathematical Physics, 1975Abstract 1. Contents 2. Introduction 3. I. Hopf's equations for the finite number degrees of freedom. 4. II. The probabilistic interpretation of Hopf's equations, characteristic functions. 5. III. Generalized characteristic functions and integrals of motion (IM). 6. IV. Integrals of motions and particular solutions. 7. V.
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Equilibrium Classical Statistical Mechanics
1984Statistical mechanics deals, as a matter of fact, with probabilistic treatment of physical systems considered from the point of view of their mechanical properties. The denomination ‘Probabilistic Mechanics’ would, of course, be more pertinent to this discipline.
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Matrices in Classical Statistical Mechanics
1966The mathematics required for formulating the principles of classical statistical mechanics does not include matrices or abstract vectors. These concepts are, however, used in applications of the general theory to specific objects. An example is considered in this chapter; it concerns the thermal properties of mixed crystals.
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Ensembles in Classical Statistical Mechanics
2012This chapter explores more powerful methods of calculation than were seen previously. Among them are Molecular Dynamics (MD) and Monte Carlo (MC) computer simulations. Another is the canonical partition function, which is related to the Helmholtz free energy.
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Statistical Mechanics of Classical Systems with Distinguishable Particles
Journal of Statistical Physics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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