In thermodynamics, Prigogine entropy is an oft-used term referring to the splitting of entropy into two variables, one being that which is "exchanged" (deS) with the surroundings and the other being a result of "internal" (diS) processes: [1]

This expression is sometimes referred to as the "Prigogine entropy equation". [2] This equation was formulated by Belgian thermodynamicist Ilya Prigogine in his 1945 Study of the Thermodynamics of Irreversible Phenomenon. This new function results, according to Prigogine, because: [3]

(a) The entropy of a system is an extensive property: if the system consists of several parts, the total entropy is equal to the sum of the entropies of each part.
(b) The change in entropy can be split into two parts: denoting deS as the flow of entropy, due to interactions with the exterior, and diS the contributions due to changes inside the system.

References
1. (a) Bailey, Kenneth D. (1990). Social Entropy Theory (term: “Prigogine entropy”, pg. 72). New York: State University of New York Press.
(b) Wang, Yingxu. (2008). Novel Approaches in Cognitive Informatics and Natural Intelligence (section: Prigogine entropy, pg. 45). Idea Group Inc.
2. Bailey, Kenneth D. (1994). Sociology and the New Systems Theory: Toward a Theoretical Synthesis (term: "Prigogine entropy equation", pg. 123). SUNY Press.
3. (a) Prigogine, Ilya. (1945). Etude Thermodynamics des Phenomenes Irreversibles (Study of the Thermodynamics of Irreversible Phenomenon). Presented to the science faculty at the Free University of Brussels (1945); Paris: Dunod, 1947.
(b) Prigogine, Ilya. (1955). Introduction to Thermodynamics of Irreversible Processes, (pg. 16). New York: Interscience Publishers.