Logical Relations among the Principles of Statistical Mechanics and Thermodynamics

Five propositions used in thermodynamics and statistical mechanics are formulated: detailed balance, microscopic reversibility, the ergodic hypothesis, the Second Law, and a restriction on the transition probabilities which will be termed the "$\lambda$ hypothesis." It is shown that the last three propositions are equivalent. The ergodic hypothesis and detailed balance together are proved to be equivalent to microscopic reversibility. This shows that microscopic reversibility is a stronger condition that the Second Law. The results are discussed in connection with Onsager's principle.