The equation of state for scalar-tensor gravity
  We show that the field equation of Brans-Dicke gravity and scalar-tensor gravity can be derived as the equation of state of Rindler spacetime, where the local thermodynamic equilibrium is maintained. Our derivation implies that the effective energy can not feel the heat flow across the Rindler horizon. 
Shao-Feng Wu, Guo-Hong Yang, Peng-Ming Zhang