Microscopic reversibility
Encyclopedia
The principle of Microscopic reversibility in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

 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
    T-symmetry
    T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

    );
  • 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.

Time-reversibility of dynamics

The Newton
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

 and the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

s in the absence of the macroscopic magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s and in the inertial frame of reference
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

 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
Configuration space
- Configuration space in physics :In classical mechanics, the configuration space is the space of possible positions that a physical system may attain, possibly subject to external constraints...

 for the Schrödinger equation).

There are two sources of the violation of this rule:
  • First, if dynamics depend of a pseudovector
    Pseudovector
    In physics and mathematics, a pseudovector is a quantity that transforms like a vector under a proper rotation, but gains an additional sign flip under an improper rotation such as a reflection. Geometrically it is the opposite, of equal magnitude but in the opposite direction, of its mirror image...

     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
    Weak interaction
    Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

     the T-symmetry may be violated and only the combined CPT symmetry
    CPT symmetry
    CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...

     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
Detailed balance
The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes : At equilibrium, each elementary process should be equilibrated by its reverse process....

 and the Onsager reciprocal relations
Onsager reciprocal relations
In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists....

.

The statistical description of the macroscopic process as an ensemble of the elementary indivisible events (collisions) was invented by L. Boltzmann
Ludwig Boltzmann
Ludwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...

 and formalised in the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...

. 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
H-theorem
In Classical Statistical Mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process. H-theorem follows from considerations of Boltzmann's equation...

 in 1872.. Later, the principle of detailed balance was developed and applied by many famous researchers.. Nowadays, it is included in most of the textbooks in statistical physics and physical chemistry.

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
Lars Onsager
Lars Onsager was a Norwegian-born American physical chemist and theoretical physicist, winner of the 1968 Nobel Prize in Chemistry.He held the Gibbs Professorship of Theoretical Chemistry at Yale University....

 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.
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