The unitarity of the universe's transition matrix implies this law because this law is a property ofdoubly stochastic Markov chains. This law is apparently in conflict with the Poincare recurrencetheorem. One consequence of this law is that the Onsager matrix is positive semi-definite, and thislaw's apparent violation of T-symmetry can be resolved using (*) Boltzmann's H-theorem. One versionof this law states that the line integral of dQ over T over a closed path is equal to or less than zero; thatstatement is Clausius' inequality. This statement limits the efficiency of the Carnot cycle and is apparentlyviolated by Maxwell's demon. For 10 po
The unitarity of the universe's transition matrix implies this law because this law is a property ofdoubly stochastic Markov chains. This law is apparently in conflict with the Poincare recurrencetheorem. One consequence of this law is that the Onsager matrix is positive semi-definite, and thislaw's apparent violation of T-symmetry can be resolved using (*) Boltzmann's H-theorem. One versionof this law states that the line integral of dQ over T over a closed path is equal to or less than zero; thatstatement is Clausius' inequality. This statement limits the efficiency of the Carnot cycle and is apparentlyviolated by Maxwell's demon. For 10 points, name this statement that says in a closed system the entropymust always increase.
The unitarity of the universe's transition matrix implies this law because this law is a property ofdoubly stochastic Markov chains.
second law of thermodynamics [accept Clausius inequality before mention]