Recently, the properties of nonequilibrium many-body quantum systems have aroused great curiosity of physicists. Numerous papers have been published about this area. But how do we measure how far the system is from equilibrium states? There are several proposals have been published, for example, using the heat which has been negated or using diagonal entropy. I am wondering whether using diagonal entropy to measure nonequilibrium has some flaws. In thermodynamics, is there a measure to describe the distance between equilibrium and nonequilibrium? Thanks so much!!