4 research outputs found
Identity of electrons and ionization equilibrium
It is perhaps appropriate that, in a year marking the 90th anniversary of
Meghnad Saha seminal paper (1920), new developments should call fresh attention
to the problem of ionization equilibrium in gases. Ionization equilibrium is
considered in the simplest "physical" model for an electronic subsystem of
matter in a rarefied state, consisting of one localized electronic state in
each nucleus and delocalized electronic states considered as free ones. It is
shown that, despite the qualitative agreement, there is a significant
quantitative difference from the results of applying the Saha formula to the
degree of ionization. This is caused by the fact that the Saha formula
corresponds to the "chemical" model of matter.Comment: 9 pages, 2 figure
Explanation of the Gibbs paradox within the framework of quantum thermodynamics
The issue of the Gibbs paradox is that when considering mixing of two gases
within classical thermodynamics, the entropy of mixing appears to be a
discontinuous function of the difference between the gases: it is finite for
whatever small difference, but vanishes for identical gases. The resolution
offered in the literature, with help of quantum mixing entropy, was later shown
to be unsatisfactory precisely where it sought to resolve the paradox.
Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining
the paradox, since it does not deal explicitly with the difference between the
gases. The proper approach employs quantum thermodynamics, which deals with
finite quantum systems coupled to a large bath and a macroscopic work source.
Within quantum thermodynamics, entropy generally looses its dominant place and
the target of the paradox is naturally shifted to the decrease of the maximally
available work before and after mixing (mixing ergotropy). In contrast to
entropy this is an unambiguous quantity. For almost identical gases the mixing
ergotropy continuously goes to zero, thus resolving the paradox. In this
approach the concept of ``difference between the gases'' gets a clear
operational meaning related to the possibilities of controlling the involved
quantum states. Difficulties which prevent resolutions of the paradox in its
entropic formulation do not arise here. The mixing ergotropy has several
counter-intuitive features. It can increase when less precise operations are
allowed. In the quantum situation (in contrast to the classical one) the mixing
ergotropy can also increase when decreasing the degree of mixing between the
gases, or when decreasing their distinguishability. These points go against a
direct association of physical irreversibility with lack of information.Comment: Published version. New title. 17 pages Revte