The principle of Microscopic reversibility in physics and chemistry is twofold:
Corresponding to every individual process there is a reverse process, and in a state of equilibrium the average rate of every process is equal to the average rate of its reverse process.[1]
The Newton and the Schrödinger equations in the absence of the macroscopic magnetic fields and in the inertial frame of reference are T-invariant: if X(t) is a solution then X(-t) is also a solution (here X is the vector of all dynamic variables, including all the coordinates of particles for the Newton equations and the wave function in the configuration space for the Schrödinger equation).
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.
The statistical description of the macroscopic process as an ensemble of the elementary indivisible events (collisions) was invented by L. Boltzmann and formalised in the Boltzmann equation. He discovered that the time-reversibility of the Newtonian dynamics leads to the detailed balance for collision: in equilibrium collisions are equilibrated by their reverse collisions. He used this principle of detailed balance to prove his famous H-theorem in 1872.[2]. Later, the principle of detailed balance was developed and applied by many famous researchers.[3][4]. Nowadays, it is included in most of the textbooks in statistical physics and physical chemistry[5].
The reciprocal relations were discovered in the 19th century by Thomson and Helmholtz for some phenomena but the general theory was proposed by Lars Onsager in 1931[6]. He found also the connection between the reciprocal relations and detailed balance. 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.