4,278 research outputs found
Thermodynamic curvature measures interactions
Thermodynamic fluctuation theory originated with Einstein who inverted the
relation to express the number of states in terms of entropy:
. The theory's Gaussian approximation is discussed in most
statistical mechanics texts. I review work showing how to go beyond the
Gaussian approximation by adding covariance, conservation, and consistency.
This generalization leads to a fundamentally new object: the thermodynamic
Riemannian curvature scalar , a thermodynamic invariant. I argue that
is related to the correlation length and suggest that the sign of
corresponds to whether the interparticle interactions are effectively
attractive or repulsive.Comment: 29 pages, 7 figures (added reference 27
Embedding initial data for black hole collisions
We discuss isometric embedding diagrams for the visualization of initial data
for the problem of the head-on collision of two black holes. The problem of
constructing the embedding diagrams is explicitly presented for the best
studied initial data, the Misner geometry. We present a partial solution of the
embedding diagrams and discuss issues related to completing the solution.Comment: (27pp text, 11 figures
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