**Macroscopic Consequences of The Time-reversibility of Dynamics**

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. This principle allowed Boltzmann to deduce simple and nice formula for entropy production and prove his famous H-theorem. Therefore, the microscopic reversibility was used to prove the macroscopic irreversibility and convergence of ensembles of molecules to their thermodynamic equilibria.

Another macroscopic consequence of microscopic reversibility is the symmetry of kinetic coefficients, the so-called reciprocal relations. 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. 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. 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. Therefore, the relaxation to equilibrium in such a system is monotone if it is sufficiently close to the equilibrium.

Read more about this topic: Microscopic Reversibility

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