Microscopic reversibility

The principle of Microscopic reversibility in physics and chemistry is twofold:

• First, it states that the microscopic detailed dynamics of particles and fields is time-reversible because the microscopic equations of motion are symmetric with respect to inversion in time (T-symmetry);
• Second, it relates to the statistical description of the kinetics of macroscopic or mesoscopic systems as an ensemble of elementary processes: collisions, elementary transitions or reactions. For these processes, the consequence of the microscopic T-symmetry is:

  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]

Time-reversibility of dynamics

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:

• First, if dynamics depend of a pseudovector like the magnetic field or the rotation angular speed in the rotating frame then the T-symmetry does not hold.
• Second, in microphysics of weak interaction the T-symmetry may be violated and only the combined CPT symmetry holds.

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. 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.

References

1. ^ Lewis, G.N. (1925) A new principle of equilibrium, PNAS March 1, 1925 vol. 11 no. 3 179-183.
2. ^ Boltzmann, L. (1964), Lectures on gas theory, Berkeley, CA, USA: U. of California Press.
3. ^ Wegscheider, R. (1911) Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reactionskinetik homogener Systeme, Monatshefte für Chemie / Chemical Monthly 32(8), 849--906.
4. ^ Einstein, A. (1916). Strahlungs-Emission und -Absorption nach der Quantentheorie [=Emission and absorption of radiation in quantum theory], Verhandlungen der Deutschen Physikalischen Gesellschaft 18 (13/14). Braunschweig: Vieweg, 318-323.
5. ^ Tolman, R. C. (1938). The Principles of Statistical Mechanics. Oxford University Press, London, UK.
6. ^ Onsager, L. (1931), Reciprocal relations in irreversible processes. I, Phys. Rev. 37, 405-426; II 38, 2265-2279