Best-guess states (e.g. for atoms in a gas) are inferred by maximizing the average surprisal S (entropy) for a given set of control parameters (like pressure P or volume V). This constrained entropy maximization, both classically and quantum mechanically, minimizes Gibbs availability in entropy units A ≡ ≡ − − k ln ⁡ ⁡ ( Z ) where Z is a constrained multiplicity or partition function.