Towards a causal effective thermodynamics of scalar-tensor gravity

The thermal analogy between the effective fluid of scalar-tensor gravity and Eckart's irreversible thermodynamics is extended to the causal Israel-Stewart model, adopting the minimal ansatz of promoting the heat flux density to a timelike vector. This choice yields analytically manageable constitutive equations, allowing for the first consistent decoupling of the effective temperature $\mathcal{T}$ and the effective thermal conductivity $\mathcal{K}$ of scalar-tensor gravity. Crucially, this new framework preserves the interpretation of general relativity as the equilibrium state approached via a dynamical relaxation process in the vanishing-$\mathcal {KT}$ limit. This new causal formalism is applied to cosmology.