In thermodynamics, non-compensated heat is a more descriptive name for entropy change dS involved in a cyclical process. The concept of “non-compensated heat”, according to Dutch thermodynamicist Sybren de Groot, was introduced by German physicist Rudolf Clausius in 1850 as a measure of irreversibility (in systems which need not be thermally insulated from their surroundings). [1] Belgian chemist Theophile de Donder, in 1927, supposedly, was able to relate Clausius’ non-compensated heat to affinity, a thermodynamic variable characterizing the state of the system. [2]

References
1. De Groot, Sybren R. and Maxur, Peter. (1961). Non-Equilibrium Thermodynamics (pgs. 1-2). New York: Dover.
2. De Donder, Theophile. (1927). L’affinite. Paris: Gauthier-Villars.

Further reading
Duhem, Pierre. (1903). Thermodynamics and Chemistry: a Non-Mathematical Treatise for Chemists and Students of Chemistry (non-compensated heat, pg. 89). J. Wiley & Sons.