Adopting the normalized d'Alembert degree-two closure (RCL) to induce real-valued costs X_ω = J(r_ω), multinomial counting and convex duality recover the finite-state Gibbs weights together with the identity F_R(q) - F_R(p) = T_R D_KL(q || p).
Cambridge University Press, 2009
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A Finite-State Gibbs Construction from a Recognition Cost
Adopting the normalized d'Alembert degree-two closure (RCL) to induce real-valued costs X_ω = J(r_ω), multinomial counting and convex duality recover the finite-state Gibbs weights together with the identity F_R(q) - F_R(p) = T_R D_KL(q || p).