Tolman's law in linear irreversible thermodynamics: a kinetic theory   approach
  In this paper it is shown that Tolman's law can be derived from relativistic kinetic theory applied to a simple fluid in a BGK-like approximation. Using this framework, it becomes clear that the contribution of the gravitational field can be viewed as a cross effect that resembles the so-called \emph{Thomson effect} in irreversible thermodynamics. A proper generalization of Tolman's law in an inhomogeneous medium is formally established based on these grounds. 
A. Sandoval-Villalbazo, A. L. Garcia-Perciante and D.Brun-Battistini
gr-qc