Editing Markov chain (section)

===Physics===
Markovian systems appear extensively in [[thermodynamics]] and [[statistical mechanics]], whenever probabilities are used to represent unknown or unmodelled details of the system, if it can be assumed that the dynamics are time-invariant, and that no relevant history need be considered which is not already included in the state description.<ref>{{cite web|title=Thermodynamics and Statistical Mechanics |first=Richard |last=Fitzpatrick |url=https://farside.ph.utexas.edu/teaching/sm1/Thermal.pdf |access-date=2017-06-02 }}</ref><ref name="auto1">{{Cite journal|last1=van Ravenzwaaij|first1=Don|last2=Cassey|first2=Pete|last3=Brown|first3=Scott D.|date=2016-03-11|title=A simple introduction to Markov Chain Monte–Carlo sampling |journal=Psychonomic Bulletin & Review |volume=25 |issue=1 |pages=143–154 |doi=10.3758/s13423-016-1015-8 |pmid=26968853 |pmc=5862921 }}</ref> For example, a thermodynamic state operates under a probability distribution that is difficult or expensive to acquire. Therefore, Markov Chain Monte Carlo method can be used to draw samples randomly from a black-box to approximate the probability distribution of attributes over a range of objects.<ref name="auto1"/>

Markov chains are used in [[lattice QCD]] simulations.<ref>{{cite book |last1= Gattringer |first1= Christof |last2= Lang |first2= Christian B |title= Quantum Chromodynamics on the Lattice |volume= 788 |doi= 10.1007/978-3-642-01850-3 |url= https://www.springer.com/gb/book/9783642018497 |publisher= Springer-Verlag Berlin Heidelberg |year= 2010 |series= Lecture Notes in Physics |isbn= 978-3-642-01849-7}}</ref>