In the mid-nineties, it has been observed by Ted Jacobson that thermodynamic equilibrium conditions applied to local, observer-dependent causal horizons encode the Einstein equations governing the gravitational dynamics. In the following decades, this observation was further developed and extended. However, it remains unclear what, if anything, it tells us about the nature of gravity. In my talk, I defend the view that, if thermodynamics encodes all the information about gravitational dynamics, it is inconsistent with general relativity. Rather it leads to Weyl transverse gravity. This theory has the same classical solutions as general relativity, but offers a different perspective on the cosmological constant, eliminating the unrealistically large vacuum energy contributions to it.