If the Hamiltonian is time-independent, { U ( t ) } form a semigroup ); this gives rise to the physical principle of detailed balance.
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In physical and chemical kinetics, T-symmetry of the mechanical microscopic equations implies two important laws : the principle of detailed balance and the Onsager reciprocal relations.
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In physics and chemistry, there are two main macroscopic consequences of the time-reversibility of microscopic dynamics : the principle of detailed balance and the Onsager reciprocal relations.
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These relations between the principle of detailed balance and the second law of thermodynamics were clarified in 1887 when Hendrik Lorentz objected to the Boltzmann H-theorem for polyatomic gases.
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For example, in the linear irreversible cycle A1-> A2-> A3-> A1, entropy production is positive but the principle of detailed balance does not hold.
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The Wegscheider conditions demonstrate that whereas the principle of detailed balance states a local property of equilibrium, it implies the relations between the kinetic constants that are valid for all states far from equilibrium.
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The extended principle of detailed balance gives an ultimate and complete answer to the following problem : " How to throw away some reverse reactions without violation of thermodynamics and microscopic reversibility ?"
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When the atoms and the radiation field are in equilibrium, the radiance will be given by Planck's law and, by the principle of detailed balance, the sum of these rates must be zero:
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In particular, he demonstrated that the irreversible cycles A1-> A2-> \ cdots-> A _ \ mathit { n }-> A1 are impossible and found explicitly the relations between kinetic constants that follow from the principle of detailed balance.
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Roughly speaking, this property, also called the principle of detailed balance, means that the probabilities to traverse a given path in one direction or in the other have a very simple connection between them ( if the graph is regular, they are just equal ).
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