Scalar-tensor gravity admits a frame-invariant perfect-fluid description with zero temperature, so that general relativity corresponds to diffusive equilibrium for both minimal and nonminimal theories.
The Thermodynamics of irreversible processes. 3.. Relativistic theory of the simple fluid
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Frame invariant diffusive formulation of scalar-tensor gravity
Scalar-tensor gravity admits a frame-invariant perfect-fluid description with zero temperature, so that general relativity corresponds to diffusive equilibrium for both minimal and nonminimal theories.