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A seldom recognized fundamental difficulty undermines the concept ofindividual ``state'' in the present formulations of quantum statisticalmechanics (and in its quantum information theory interpretation as well). Thedifficulty is an unavoidable consequence of an almost forgotten corollaryproved by E. Schroedinger in 1936 and perused by J.L. Park, Am. J. Phys., Vol.36, 211 (1968). To resolve it, we must either reject as unsound the concept ofstate, or else undertake a serious reformulation of quantum theory and the roleof statistics. We restate the difficulty and discuss a possible resolutionproposed in 1976 by G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol.6, 15, 127, 439, 561 (1976).Comment: RevTeX4, 7 pages, corrected a paragraph and added an example at page  3, to appear in Mod. Phys. Lett.

THE HATSOPOULOS–GYFTOPOULOS RESOLUTION OF THE SCHRÖDINGER–PARK PARADOX ABOUT THE CONCEPT OF "STATE" IN QUANTUM STATISTICAL MECHANICS