Editing Master equation (section)

{{Short description|Equations governing time evolution of physical systems}}
{{about||the master equation used in quantum physics|Lindblad equation|the master equations in Lagrangian gauge theory|Batalin–Vilkovisky formalism|the master theorem for analyzing algorithmic complexity|Master theorem (analysis of algorithms)}}
{{More footnotes needed|date=June 2011}}

In [[physics]], [[chemistry]], and related fields, '''master equations''' are used to describe the [[time evolution]] of a system that can be modeled as being in a [[probability|probabilistic]] combination of states at any given time, and the switching between states is determined by a [[transition rate matrix]]. The equations are a set of [[differential equations]] &ndash; over time &ndash; of the probabilities that the system occupies each of the different states.

The name was proposed in 1940:<ref>{{Cite journal |last=Cohen |first=E. G. D. |date=July 1990 |title=George E. Uhlenbeck and statistical mechanics |url=https://pubs.aip.org/aapt/ajp/article/58/7/619-625/1043995 |journal=American Journal of Physics |language=en |volume=58 |issue=7 |pages=619–625 |doi=10.1119/1.16504 |bibcode=1990AmJPh..58..619C |issn=0002-9505|url-access=subscription }}</ref><ref>{{Cite journal |last1=Nordsieck |first1=A. |last2=Lamb |first2=W.E. |last3=Uhlenbeck |first3=G.E. |date=1940 |title=On the theory of cosmic-ray showers I: The Furry model and the fluctuation problem |url=https://www.sciencedirect.com/science/article/abs/pii/S0031891440901021 |journal=Physica |language=en |volume=7 |issue=4 |pages=344–360 |doi=10.1016/S0031-8914(40)90102-1|bibcode=1940Phy.....7..344N |hdl=2027.42/32597 |hdl-access=free }}</ref>
{{Blockquote
 | text = ''When the probabilities of the elementary processes are known, one can write down a continuity equation for W, from which all other equations can be derived and which we will call therefore the "master” equation.''
 | title = "On the theory of cosmic-ray showers I: The [[Wendell H. Furry|Furry]] model and the fluctuation problem" (1940)
 | author = Nordsieck, Lamb, and Uhlenbeck }}