According to a recently given ergodic condition for Hermitian many-body models the thermodynamic limit and irreversibility are necessary but by themselves not sufficient. The sufficient condition turns out to be the existence of a zero-frequency mode. It is measured by an infinite product of the...

The independent-oscillator model is thought to be a simple model for Brownian motion, explored extensively by Ford, Lewis and O'Connell. This model does not specify the distribution of the oscillators’ frequencies. By considering the distribution to be of two standard limits, otherwise...

Ideal quantum gases have been historically studied separately according to whether they obey Bose or Fermi statistics. It has been found that their statistical thermodynamics can be unified by means of polylogs, certain transcendental functions. The unified formalism is used to show that in two...

The exact high temperature series expansion for the longitudinal susceptibility of the spin-12 XY model is given. An expansion for a related quantity, the reduced susceptibility, is also obtained by noting a simple relationship between the two susceptibilities. Both series are nondivergent. The...