[3] In chemistry, J. H. van't Hoff (1884)[4] came up with the idea that equilibrium has dynamical nature and is a result of the balance between the forward and backward reaction rates.
Lars Onsager (1931) used these relations in his well-known work,[6] without direct citation but with the following remark: "Here, however, the chemists are accustomed to impose a very interesting additional restriction, namely: when the equilibrium is reached each individual reaction must balance itself.
Sometimes, the principle of detailed balance is formulated in the narrow sense, for chemical reactions only[8] but in the history of physics it has the broader use: it was invented for collisions, used for emission and absorption of quanta, for transport processes[9] and for many other phenomena.
There are two sources of the violation of this rule: 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.
This principle allowed Boltzmann to deduce simple and nice formula for entropy production and prove his famous H-theorem.
For the equations of the law of mass action the reciprocal relations appear in the linear approximation near equilibrium as a consequence of the detailed balance conditions.
According to the reciprocal relations, the damped oscillations in homogeneous closed systems near thermodynamic equilibria are impossible because the spectrum of symmetric operators is real.