  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.
