One extension of this law states that the ratio of the probability of a pair of time-averaged dissipation functions is equal to an exponential; that theorem gives the probability of microscopically violating this law and is called the (*) fluctuation theorem.
One generalization of this statement can be used to derive Landauer's principle. One consequence of this law is that the matrix L in the Onsager reciprocal relations is positive-definite. One extension of this law states that the ratio of the probability of a pair of time-averaged dissipation functions is equal to an exponential; that theorem gives the probability of microscopically violating this law and is called the (*) fluctuation theorem. One method of deriving this statement is to take a closed line integral of dQ over T for an irreversible process; that gives an inequality named for Clausius. A creature that could sort fast particles from slow ones would violate this law; that creature is Maxwell's demon. This law limits the efficiency of the Carnot cycle. For 10 points, name this law which states that for a closed system, the entropy always increases.
One generalization of this statement can be used to derive Landauer's principle.
Second Law of Thermodynamics