Second law of thermodynamics and Configurational Mechanics

Hello,

I have been reading up a lot on "Configurational Mechanics" and frankly i came up with a lot of questions. I am not skeptical at all about it, it just that many things are not clear to me.

Indeed i think that something important is missing in that framework: the laws of thermodynamics. The Eshelby tensor Σ was introduced by calculating the change of energy  due to the shifting of a defect by an amount δX
while the boundary conditions remain the same. And that change of
energy is thus not a physical quantity. What it is exactly and what it
thermodynamically represents? Frankly i don't know....

I even wonder if it has to be positive or negative? I mean as for
the second law of thermodynamics that predicts the direction of
evelution of the physical system, there should be a kind of "material
law of thermodynamics" that can predict the direction of evolution of
the material system, i.e. of that change of energy when the defect is
shifted.

Because up till now, other than equations (balance law projected
onto the material manifold) i have never heard of a  kind of law of
thermodynamics in the material manifold giving the direction of
evolution between two reference configurations. I am really interested
in knowing if someone tried to build up such a "material law of
thermodynamics.

Any comment or information will be very useful.

Thanks,

Malik