Historically - - -
Planck: We have now to seek a physical quantity whose magnitude shall serve as a general measure of the preference of nature for a given state. ...... R. Clausius actually found this quantity and called it "entropy". ..... Conduction of heat to a body increases its entropy, and , in fact, by an amount equal to the ration of the quantity of heat given the body to its temperature. Simple compression, on the other hand, does not change it entropy. ......In the limiting case, a reversible isothermal cyclical process, the sign of the (heat) equality holds, and therefore the work consumed is zero, and also the heat produced. This law plays a leading role in the applications of thermodynamics to physical chemistry. ..... The second law of thermodynamics imposes further limitations to the first law, allowing only certain types of transformations subject to certain conditions. in accordance with this law,
the some of Q/T is equal to or greater than zero. Heat is produced and work is consumed. In the limiting case, the work consumed is zero, the produced is zero, and the equality holds." Q = heat.
Planck's equation for the general law of entropy is S - (U + pV)/T = phi = dU +pdV where phi is the phase of the system and is linear and homogenous in S, U and V. S in the entropy, and U is the energy.
Entropy is "... a measure of the preference of nature for a given energy state". Planck used this concept to define the energy states of chemical reactions, which was the foundation of the development of his radiation equation. It is not clear to me as to how you can apply the concept of entropy to an engine.