The differential of internal energy equals P dV plus mu dN plus temperature times the differential of this quantity.
A paper by Wald claims that this quantity is the Noether charge associated with diffeomorphism invariance. One formula for this quantity has a term proportional to the natural logarithm of volume times mass and internal energy both raised to the three halves power. The fluctuation theorem governs this quantity's dynamics when at non-equilibrium conditions, and it's proportional to the area of the event horizon for black holes. The differential of internal energy equals P dV plus mu dN plus temperature times the differential of this quantity. This quantity is zero for a perfect crystal at absolute zero according to the third law of thermodynamics and it doesn't change in a reversible process. For 10 points, name this quantity which always increases according to the second law of thermodynamics.
A paper by Wald claims that this quantity is the Noether charge associated with diffeomorphism invariance.
entropy [accept specific things like Wald entropy, Bekenstein entropy, Black hole entropy]