Dynamical systems and thermodynamics

[JRR]

Is there a mathematical way to show that a dissipative (or general?) dynamical system obeys the laws of thermodynamics?

I am looking for books/sites/references, thanks for any reply.

 

[russ_watters]

Probably. Can you be more specific/detailed?

 

[JRR]

Thanks for your reply.
The system would typically be the development of stress versus time, or alternatively stress versus strain for a given strain rate.
The simplest form I could think of is this (two variants, as described above):

Where σ is the stress, t is time, ε is strain and k_t and k_ε are constants.