Editing Microcanonical ensemble (section)

== Applicability ==

Because of its connection with the elementary assumptions of equilibrium statistical mechanics (particularly the [[Principle of indifference|postulate of a priori equal probabilities]]), the microcanonical ensemble is an important conceptual building block in the theory.<ref name="Balescu1975">{{Citation|last1=Balescu|first1=Radu|author-link=Radu Bălescu|title=Equilibrium and Nonequilibrium Statistical Mechanics|publisher=John Wiley & Sons|year=1975|isbn=978-0-471-04600-4}}</ref> It is sometimes considered to be the fundamental distribution of equilibrium statistical mechanics. It is also useful in some numerical applications, such as [[molecular dynamics]].<ref name="PearsonHalicioglu1985">{{cite journal|last1=Pearson|first1=Eric M.|last2=Halicioglu|first2=Timur|last3=Tiller|first3=William A.|title=Laplace-transform technique for deriving thermodynamic equations from the classical microcanonical ensemble|journal=Physical Review A|volume=32|issue=5|year=1985|pages=3030–3039|issn=0556-2791|doi=10.1103/PhysRevA.32.3030|pmid=9896445 |bibcode=1985PhRvA..32.3030P }}</ref><ref name="Lustig1994">{{cite journal|last1=Lustig|first1=Rolf|title=Statistical thermodynamics in the classical molecular dynamics ensemble. I. Fundamentals|journal=The Journal of Chemical Physics|volume=100|issue=4|year=1994|pages=3048–3059|issn=0021-9606|doi=10.1063/1.466446|bibcode=1994JChPh.100.3048L |doi-access=free}}</ref> On the other hand, most nontrivial systems are mathematically cumbersome to describe in the microcanonical ensemble, and there are also ambiguities regarding the definitions of entropy and temperature. For these reasons, other ensembles are often preferred for theoretical calculations.<ref name="Balescu1975" /><ref name="Hill1986">{{cite book|title=An Introduction to Statistical Thermodynamics|first=Terrell L.|last=Hill|publisher=Dover Publications|year=1986|isbn=978-0-486-65242-9}}</ref><ref>{{cite book|title=Statistical Mechanics|first=Kerson|last=Huang|publisher=John Wiley & Sons|year=1967}}</ref>

The applicability of the microcanonical ensemble to real-world systems depends on the importance of energy fluctuations, which may result from interactions between the system and its environment as well as uncontrolled factors in preparing the system. Generally, fluctuations are negligible if a system is macroscopically large, or if it is manufactured with precisely known energy and thereafter maintained in near isolation from its environment.<ref name="HilbertHänggi2014">{{cite journal|last1=Hilbert|first1=Stefan|last2=Hänggi|first2=Peter|last3=Dunkel|first3=Jörn|title=Thermodynamic laws in isolated systems|journal=Physical Review E|volume=90|issue=6|year=2014|page=062116 |issn=1539-3755|doi=10.1103/PhysRevE.90.062116|pmid=25615053 |arxiv=1408.5382 |bibcode=2014PhRvE..90f2116H |hdl=1721.1/92269|s2cid=5365820 |hdl-access=free}}</ref> In such cases the microcanonical ensemble is applicable. Otherwise, different ensembles are more appropriate – such as the [[canonical ensemble]] (fluctuating energy) or the [[grand canonical ensemble]] (fluctuating energy and particle number).