Let uϕ u_{\phi}uϕ and uψ u_{\psi}uψ be free Gibbs measures associated with strictly C2\mathcal{C}^2C2 convex potentials ϕ,ψ:R→R\phi,\psi:\mathbb{R}\rightarrow\mathbb{R}ϕ,ψ:R→R, and write…