Term information
In physics, a master equation is a phenomenological set of first-order[citation needed] differential equations describing the time evolution of the probability of a system to occupy each one of a discrete set of states[citation needed]: \frac{dP_k}{dt}=\sum_\ell T_{k\ell}P_\ell, where Pk is the probability for the system to be in the state k, while the matrix T is filled with a grid of transition-rate constants. source: http://en.wikipedia.org/wiki/Master_equation
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mfenced close="" open=""> <mrow> <mfrac> <mrow> <mi>d</mi> <mo>⁢</mo> <msub> <mi>P</mi> <mi>k</mi> </msub> </mrow> <mrow> <mi>d</mi> <mo>⁢</mo> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mrow> <munder> <mo>∑</mo> <mi>ℓ</mi> </munder> <mo>⁢</mo> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mo>⁢</mo> <mi>ℓ</mi> </mrow> </msub> <mo>⁢</mo> <msub> <mi>P</mi> <mi>ℓ</mi> </msub> </mrow> </mrow> </mfenced> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <mfrac> <mrow> <mi>d</mi> <msub> <mi>P</mi> <mi>k</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <munder> <mo>∑</mo> <mi>ℓ</mi> </munder> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mi>ℓ</mi> </mrow> </msub> <msub> <mi>P</mi> <mi>ℓ</mi> </msub> <mo>,</mo> </mrow> <annotation encoding="SnuggleTeX">\[ \frac{dP_k}{dt}=\sum_\ell T_{k\ell}P_\ell, \]</annotation> </semantics> </math>