Stating that entropy reaches a maximum at equilibrium, for 10 points, give this statement that an isolated system's entropy will tend to increase.
The Clausius-Duhem inequality recasts this statement in the terms of continuum mechanics. Loschmidt's paradox is an objection to another formulation of this statement. That formulation states that the derivative of a function given as the sum over all microstates of that state's probability p times the natural log of p is always positive and is called Boltzmann's H-theorem. The suggestion that heat does not generally spontaneously flow from low -to high-temperature objects is the Clausius formation of this statement. Stating that entropy reaches a maximum at equilibrium, for 10 points, give this statement that an isolated system's entropy will tend to increase.
The Clausius-Duhem inequality recasts this statement in the terms of continuum mechanics.
{second law} of thermodynamics [accept {Boltzmann's H}-{theorem} before mention]