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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 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 – over time – of the probabilities that the system occupies each of the different states.
The name was proposed in 1940:[1][2]
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.
— Nordsieck, Lamb, and Uhlenbeck, "On the theory of cosmic-ray showers I the furry model and the fluctuation problem" (1940)
- ^ Cohen, E. G. D. (July 1990). "George E. Uhlenbeck and statistical mechanics". American Journal of Physics. 58 (7): 619–625. Bibcode:1990AmJPh..58..619C. doi:10.1119/1.16504. ISSN 0002-9505.
- ^ Nordsieck, A.; Lamb, W.E.; Uhlenbeck, G.E. (1940). "On the theory of cosmic-ray showers I the furry model and the fluctuation problem". Physica. 7 (4): 344–360. Bibcode:1940Phy.....7..344N. doi:10.1016/S0031-8914(40)90102-1. hdl:2027.42/32597.