In information thermodynamics, Szilard’s paradox refers to paradoxical similarity between the formal definitions of entropy used in statistical thermodynamics
and information theory, namely Boltzmann entropy and Shannon entropy, which has misled many authors to identify entropy of information with negative physical entropy. [1] The origin of the confusion said to have originated with Hungarian-born American physicist Leó Szilárd’s 1929 seemingly paradoxical thought experiment concerning Maxwell’s demon. [2] The term “Szilard’s paradox” seems to have been introduced in the 1972 article “Entropy, Information, and Szilard’s Paradox” by mathematical physicists Josef M. Jauch and J.G. Baron, who attempted to explain that there is no paradox.

References
1. Jauch, J.M. and Baron, J.G. (1972). “Entropy, Information, and Szilard’s Paradox”, Helv Phys Acta, 45: 220-32; In: Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing (pgs. 124-36). CRC Press, 2003.
2. (a) Szilárd, Leó. (1929). “On the Decrease in Entropy in a Thermodynamic System by the Intervention of Intelligent Beings”, Zeitschrift fur Physik, 53, pgs. 840-56.
(b) English translation of “On the Decrease in Entropy in a Thermodynamic System by the Intervention of Intelligent Beings” by Anatol Rapoport and Mechthilde Knoller in Maxwell’s Demon 2 (pgs. 110-19) by Harvey Leff and Andrew Rex.