Editing Master equation (section)

==Examples of master equations==
Many physical problems in [[classical mechanics|classical]], [[quantum mechanics]] and problems in other sciences, can be reduced to the form of a ''master equation'', thereby performing a great simplification of the problem (see [[mathematical model]]).

The [[Lindblad equation]] in [[quantum mechanics]] is a generalization of the master equation describing the time evolution of a [[density matrix]].  Though the Lindblad equation is often referred to as a ''master equation'', it is not one in the usual sense, as it governs not only the time evolution of probabilities (diagonal elements of the density matrix), but also of variables containing information about [[quantum coherence]] between the states of the system (non-diagonal elements of the density matrix).

Another special case of the master equation is the [[Fokker–Planck equation]] which describes the time evolution of a [[continuous probability distribution]].<ref>{{cite book|last1=Honerkamp|first1=Josef|title=Statistical physics : an advanced approach with applications; with 7 tables and 57 problems with solutions|url=https://archive.org/details/statisticalphysi00hone_604|url-access=limited|date=1998|publisher=Springer|location=Berlin [u.a.]|isbn = 978-3-540-63978-7 | pages=[https://archive.org/details/statisticalphysi00hone_604/page/n180 173]}}</ref> Complicated master equations which resist analytic treatment can be cast into this form (under various approximations), by using approximation techniques such as the [[system size expansion]].

Stochastic [[chemical kinetics]] provide yet another example of the use of the master equation. A master equation may be used to model a set of chemical reactions when the number of molecules of one or more species is small (of the order of 100 or 1000 molecules).<ref>{{Cite journal|last1=Gupta|first1=Ankur|last2=Rawlings|first2=James B.|date=Apr 2014|title=Comparison of Parameter Estimation Methods in Stochastic Chemical Kinetic Models: Examples in Systems Biology|journal=AIChE Journal|volume=60|issue=4|pages=1253–1268|doi=10.1002/aic.14409|issn=0001-1541|pmc=4946376|pmid=27429455|bibcode=2014AIChE..60.1253G }}</ref> The chemical master equation can also solved for the very large models, such as the DNA damage signal from fungal pathogen Candida albicans.<ref>{{Cite journal|last1=Kosarwal|first1=Rahul|last2=Kulasiri|first2=Don|last3=Samarasinghe|first3=Sandhya|date=Nov 2020|title=Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks|journal=BMC Bioinformatics |volume=21 |issue=1 |page=515 |doi=10.1186/s12859-020-03668-2 |pmid=33176690 | pmc=7656229 |doi-access=free }}</ref>