The Jarzynski equality (JE) is an equation in statistical mechanics that relates free energy differences between two equilibrium states and non-equilibrium processes. It is named after the physicist Christopher Jarzynski (then at Los Alamos National Laboratory) who derived it in 1997. source: http://en.wikipedia.org/wiki/Jarzynski_equality

Jarzynski equality

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mrow> <mi>&Delta;</mi> <mo>&InvisibleTimes;</mo> <mi>F</mi> </mrow> <mo>/</mo> <mrow> <mi>k</mi> <mo>&InvisibleTimes;</mo> <mi>T</mi> </mrow> </mrow> </mrow> </msup> <mo>=</mo> <mover accent="true"> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mi>W</mi> <mo>/</mo> <mrow> <mi>k</mi> <mo>&InvisibleTimes;</mo> <mi>T</mi> </mrow> </mrow> </mrow> </msup> <mo>¯</mo> </mover> </mrow> </math>

e^ { -\Delta F / k T} = \overline{ e^{ -W/kT } }

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>&Delta;</mi> <mi>F</mi> <mo>/</mo> <mi>k</mi> <mi>T</mi> </mrow> </msup> <mo>=</mo> <mover accent="true"> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>W</mi> <mo>/</mo> <mi>k</mi> <mi>T</mi> </mrow> </msup> <mo>¯</mo> </mover> </mrow> <annotation encoding="SnuggleTeX">\[ e^ { -\Delta F / k T} = \overline{ e^{ -W/kT } } \]</annotation> </semantics> </math>