On entropy in eulerian thermodynamics
  To the student of thermodynamics the most difficult subject is entropy. In this paper we examine the actual, practical application of entropy to two simple systems, the homogeneous slab with fixed boundary values of the temperature, and an isolated atmosphere in the presence of the static gravitational field. The first gives valuable insight into the nature of entropy that is subsequently applied to the second system.   It is a basic tenet of thermodynamics that the equilibrium of an extended, homogeneous and isolated system is characterized by a uniform temperature distribution and it is a strongly held belief that this remains true in the presence of gravity. We find that this is consistent with the equations of extended thermodynamics but that entropy enters in an essential way. The principle of equivalence takes on a new aspect. 
Christian Fr{\o}nsdal, Abhishek Pathak
cond-mat.stat-mech