An irreversible thermodynamics treatment of plastic deformation is re-formulated to include the effects of steel chemistry in austenite hot rolling. By relating the entropy to the relevant fluxes and forces, the assumption dS ∝ d τ / T is removed, where S and τ are the entropy and stress at temperature T. The effect of composition is incorporated in the activation energy for cross-slip, obtaining a good description of the stress-strain behaviour of various grades as a function of temperature and strain rate.