Pauli problem in thermodynamics

A thermodynamic analogue of the Pauli problem (reconstruction of a wavefunction from the position and momentum distributions) is formulated. The coordinates of a quantum system are replaced by the inverse absolute temperature and other intensive quantities, and the Planck constant is replaced by the Boltzmann constant multiplied by two. A new natural mathematical generalization of the quasithermodynamic fluctuation theory is suggested and sufficient conditions for the existence of asymptotic solutions of the thermodynamic Pauli problem are obtained.