TABLE OF CONTENTS Consider an ideally elastic, homogeneous (although perhaps anisotropic) medium. Hooke s law relating stress ? ij to strain ? k ? can be written
where c ij k ? is the tensor of elastic stiffnesses. Alternatively, one can write
where c ij k ? is the tensor of elastic compliances. The stiffness and compliance tensors are mutually inverse, and both are positive definite. In our language, they are Jeffreys tensors. Because of the different symmetries among their components, there are only 21 degrees of freedom to represent an ideally elastic medium. There are many possible choices for the 21 quantities needed to represent an elastic medium. But whatever our choice for these quantities, there is one general answer to the problem of obtaining the associated homogeneous probability density.
In the 21-dimensional abstract space where each point represents one elastic medium, there is only one choice of distance between two points (i.e., between two elastic media) that has all the necessary invariances (it must satisfy the axioms of a distance, the expression has to be the same when using stiffness or compliance, there must be invariance of scale). The distance between the elastic medium 
(represented by the stiffness tensor c 1 or the compliance tensor s 1) and the elastic medium 
(represented by the stiffness tensor c 2 or the compliance tensor s 2) is
One should remember here that the logarithm of...
