It is remarkable that Cartan's magic formula leads to a dynamic realization of the first law of thermodynamics.

L(V)A = W + dU = Q

From classical thermodynamics, a process is irreversible if the heat 1-form Q does not admit an integrating factor.

But Q does not admit an integration factor id Q^dQ <>0.

Hence, given a physical system A, just solve for those processes V such that Q^dQ <> 0 and you know that the process is thermodynamically irreversible.

In the download below, details are given. It would appear that irreversibility is an artifact of 4 dimensions or more.

Irreversible Evolution

As I have time I will replace this under construction symbol with a link to a more detailed pdf or tex file download.