Thermodynamic integration: Difference between revisions
Carl McBride (talk | contribs) m (New page: Used to calculate the free energy difference between two states. The path must be ''continuous'' and ''reversible''. One has a continuously variable energy function <math>U_\lambda</math>...) |
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The path must be ''continuous'' and ''reversible''. | The path must be ''continuous'' and ''reversible''. | ||
One has a continuously variable energy function <math>U_\lambda</math> such that | One has a continuously variable energy function <math>U_\lambda</math> such that | ||
<math>\lambda=0</math>, <math>U_\lambda=U_0</math> | <math>\lambda=0</math>, <math>U_\lambda=U_0</math> and <math>\lambda=1</math>, <math>U_\lambda=U</math> | ||
and | |||
<math>\lambda=1</math>, <math>U_\lambda=U</math> | |||
<math>\Delta A = A - A_0 = \int_0^1 d\lambda | :<math>\Delta A = A - A_0 = \int_0^1 d\lambda \langle\frac{\partial U_\lambda}{\partial \lambda}\rangle_{\lambda}</math> | ||
:<math>\left.U_\lambda\right.=(1-\lambda)U_0 + \lambda U</math> | |||
<math>U_\lambda=(1-\lambda)U_0 + \lambda U</math> | |||
Revision as of 11:35, 23 February 2007
Used to calculate the free energy difference between two states. The path must be continuous and reversible. One has a continuously variable energy function Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U_{\lambda }} such that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda=0} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U_\lambda=U_0} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda=1} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U_\lambda=U}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta A = A - A_0 = \int_0^1 d\lambda \langle\frac{\partial U_\lambda}{\partial \lambda}\rangle_{\lambda}}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.U_\lambda\right.=(1-\lambda)U_0 + \lambda U}