Editing Perron–Frobenius theorem (section)

===Compact operators===
{{main|Krein–Rutman theorem}}
More generally, it can be extended to the case of non-negative [[compact operator]]s, which, in many ways, resemble finite-dimensional matrices. These are commonly studied in physics, under the name of [[transfer operator]]s, or sometimes '''Ruelle–Perron–Frobenius operators''' (after [[David Ruelle]]). In this case, the leading eigenvalue corresponds to the [[thermodynamic equilibrium]] of a [[dynamical system]], and the lesser eigenvalues to the decay modes of a system that is not in equilibrium. Thus, the theory offers a way of discovering the [[arrow of time]] in what would otherwise appear to be reversible, deterministic dynamical processes, when examined from the point of view of [[point-set topology]].<ref>{{cite book |first=Michael C. |last=Mackey |title=Time's Arrow: The origins of thermodynamic behaviour |location=New York |publisher=Springer-Verlag |year=1992 |isbn=978-0-387-97702-7 }}</ref>