Related papers: Boltzmann entropy and the microcanonical ensemble
Phase transitions in nuclei, small atomic clusters and self-gravitating systems demand the extension of thermo-statistics to ``Small'' systems. The main obstacle is the thermodynamic limit. It is shown how the original definition of the…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
Extensive body of work has shown that for the model of a non-interacting electron in a random potential there is a quantum critical point for dimensions greater than two---a metal-insulator transition. This model also plays an important…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Critical-point Hamiltonians for first- and second-order transitions are identified by resolving them into intrinsic and…
A system of bosons studied within the mean field framework has two fascinating phenomena: a liquid-gas first order phase transition and Bose-Einstein condensation. Interplay between these two phenomena is being investigated. Depending on…
Microcanonical thermodynamics (MT) is analysed for phase transitions of first and second order in finite systems. The transiton temperature, the latent heat and the surface tension of first order transitions can easily be determined by MT…
It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighbourhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states,…
The study of critical phenomena and phase transitions is an important part of modern condensed matter physics. In this regard, the phenomenological Landau theory has been extraordinarily useful. Hereby we present an alternative theoretical…
This contribution inquires into Clausius' proposal that "the entropy of the world tends to a maximum.'" The question is raised whether the entropy of "the world" actually does have a maximum; and if the answer is "Yes!," what such states of…
Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulae for the microcanonical partition functions in the case of non-interacting massless neutral particles…
We study many-body phase transitions in a one-dimensional ferromagnetic transversed field Ising model with an imaginary field and show that the system exhibits three phase transitions: one second-order phase transition and two…
Using the average method, we derive a close set of linear equations that describes the spinning up of an harmonically trapped gas by a rotating anisotropy. We find explicit expressions for the needed to transfer angular momentum as well as…
One of the few accepted dynamical foundations of non-additive "non-extensive") statistical mechanics is that the choice of the appropriate entropy functional describing a system with many degrees of freedom should reflect the rate of growth…
We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has…
A lower bound on the R\'enyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the…
Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
The microscopic derivation of the second law for macroscopic system is given under the phenomenological assumption that both the initial and final states are described by mutually different canonical ensembles. In particular, it is also…
We study the motion of a particle in a plane subject to an attractive central force with inverse-square law on one side of a wall at which it is reflected elastically. This model is a special case of a class of systems considered by…