An Etymological Dictionary of Astronomy and Astrophysics

The ordinary Newtonian energy conservation equation when expressed in expanding cosmological coordinates. More specifically, it is the relation between the → kinetic energy per unit mass associated with the motion of matter relative to the general → expansion of the Universe and the → gravitational potential energy per unit mass associated with the departure from a homogeneous mass distribution. In other words, it deals with how the energy of the → Universe is partitioned between kinetic and potential energy.
Also known as → cosmic energy equation.
In its original form, the Layzer-Irvine equation accounts for the evolution of the energy of a system of → non-relativistic particles, interacting only through gravity, until → virial equilibrium

is reached. But it has recently been generalized to account for interaction between → dark matter and a homogeneous → dark energy component. Thus,
it describes the dynamics of local dark matter perturbations in an otherwise homogeneous and → isotropic Universe (P. P. Avelino and C. F. V. Gomes, 2013, arXiv:1305.6064).

See also: W. M. Irvine, 1961, Ph.D. thesis, Harvard University; D. Layzer, 1963, Astrophys. J. 138, 174; → equation.