1 research outputs found
Thermodynamics with long-range interactions: from Ising models to black-holes
New methods are presented which enables one to analyze the thermodynamics of
systems with long-range interactions. Generically, such systems have entropies
which are non-extensive, (do not scale with the size of the system). We show
how to calculate the degree of non-extensivity for such a system. We find that
a system interacting with a heat reservoir is in a probability distribution of
canonical ensembles. The system still possesses a parameter akin to a global
temperature, which is constant throughout the substance. There is also a useful
quantity which acts like a {\it local temperatures} and it varies throughout
the substance. These quantities are closely related to counterparts found in
general relativity. A lattice model with long-range spin-spin coupling is
studied. This is compared with systems such as those encountered in general
relativity, and gravitating systems with Newtonian-type interactions. A
long-range lattice model is presented which can be seen as a black-hole analog.
One finds that the analog's temperature and entropy have many properties which
are found in black-holes. Finally, the entropy scaling behavior of a
gravitating perfect fluid of constant density is calculated. For weak
interactions, the entropy scales like the volume of the system. As the
interactions become stronger, the entropy becomes higher near the surface of
the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22
pages, 2 figure