Typically, we assume that macroscopic energy fluctuations can occur a little bit. This gives us uncertainty in energy, and allows us to predict the order at which events occured in time. If we introduce the concept of Quantropy into stat mech, we could get a better, more accurate path integral description. If quantropy is able to be massaged into entropy, then we can make an effective classical theory which takes into account all of the quantum mechanical fluctuations perfectly. This sounds way too good to be true.
Quantropy is mathematically: http://arxiv.org/pdf/1311.0813v2.pdf
Physically, it is required in a quantum mechanical path integral for complex systems such as computers or humans with memory.