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Mathematics and Its ApplicationsIn this chapter, the grand canonical ensemble describing a system that exchanges energy and particles with the external world is introduced. The density fluctuations at the critical point and the ideal quantum boson and fermion gases are presented as key applications of this ensemble.
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MechanicsIn this first chapter, some of the basic concepts of Hamiltonian mechanics (both classical and quantum mechanical), which are required for the study of statistical physics, are summarized. For a more detailed analysis of these topics the reader is referred to the books included in the References.
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Microcanonical EnsembleIn this chapter the microcanonical ensemble microcanonical ensemble, which describes an isolated system, is introduced. In this ensemble the entropy and the temperature, i.e. the fundamental thermal variables of thermodynamics, are defined.
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Grand Canonical EnsembleIn this chapter, the grand canonical ensemble describing a system that exchanges energy and particles with the external world is introduced. The density fluctuations at the critical point and the ideal quantum boson and fermion gases are presented as key applications of this ensemble.
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https://doi.org/10.1007/978-3-030-10430-6description of a system. In the first case, the mechanical state of . material points at time t is determined by 3. generalized coordinates and their 3. conjugate momenta (classical mechanics) or by the wave function (quantum mechanics). In the second instance, the equilibrium state of a simple clos
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Some General Results in Stability Theory,entropy is the thermodynamic potential associated to this ensemble. The microcanonical ensemble presents two types of difficulties. The first one is mathematical since, even in the simplest systems, determining the entropy is not a trivial issue. The second difficulty is that the systems studied in
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Location Models for Preventive Caree-particle dynamical functions and of one-particle operators (kinetic energy and harmonic oscillators). Real systems are characterized by the fact that, besides the kinetic energy, H.(q,p;α ) and Ĥ.(α ) also include the potential energy, which describes how the particles, atoms or molecules, interac
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Applications of Logic Databaseson of its microscopic constituents. Note that in this context microscopic may have different meanings. Indeed, although it is common to consider that matter is made of atoms or molecules (something known as the atomic description atomic description), this is not the only possible description. For in
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