Master equation: Difference between revisions

Revision as of 15:32, 26 June 2008

The master equation describes the exact behavior of the velocity distribution for any time (Ref. 1 Eq. 3-11)

\partial _{t\rho _{0}}\left(\{{\mathbf {\upsilon } }\},t\right)={\mathcal {D}}_{0}\left(t,\rho _{\{k''\}}\left(\{{\mathbf {\upsilon } }\},0\right)\right)+\int _{0}^{t}G_{00}(t-t')\rho _{0}\left(\{{\upsilon }\},t'\right){\mathrm {d} }t'

where

{\mathcal {D}}_{0}\left(t,\rho _{\{k''\}}\left(\{{\mathbf {\upsilon } }\},0\right)\right)

@@ Line 1: / Line 1: @@
 {{stub-general}}
+The '''master equation''' describes the exact behavior of the velocity distribution for any time (Ref. 1 Eq. 3-11)
+:<math>\partial_{t \rho_0} \left( \{ {\mathbf \upsilon} \},t \right) =  {\mathcal D}_0 \left(t, \rho_{ \{k'' \} } \left( \{ {\mathbf \upsilon} \},0 \right)  \right) + \int_0^t G_{00}(t-t') \rho_0 \left( \{ {\upsilon} \},t' \right)  {\mathrm d}t'</math>
+where
+:<math>{\mathcal D}_0 \left(t, \rho_{ \{k'' \} } \left( \{ {\mathbf \upsilon} \},0 \right)  \right)</math>
 ==References==
 #[http://dx.doi.org/10.1016/0031-8914(61)90008-8 I. Prigonine and P. Résibois "On the kinetics of the approach to equilibrium", Physica '''27''' pp. 629-646  (1961)]
 [[category: Non-equilibrium thermodynamics]]