  We construct the thermodynamics of energy magnetization in the presence of
gravitomagnetic field. We show that the free energy must be modified to account
for the modification of the energy current operator in the presence of a
confining potential. The explicit expression of the energy magnetization is
derived for a periodic system, and the Streda formula for the thermal Hall
conductivity is rigorously established. We demonstrate our theory of the energy
magnetization and the Streda formula in a Chern insulator.
