Legendre-transform structure derived from quantum theorems

► From two purely quantum mechanical theorems, the virial and the Feynman-Hellman ones, Jaynes' information theoretical reciprocity relations are derived. ► These relations involve the coefficients of a series-expansion of the potential function appearing in Schrödinger's equation instead of the intensive variables of thermodynamics. ► This demonstrates the existence of a Legendre-transform structure behind Schrödinger's equation, akin to the one characterizing thermodynamics.