Thermodynamic integration

Used to calculate the free energy difference between two states. The path must be continuous and reversible. One has a continuously variable energy function $U_{\lambda }$ such that $\lambda =0$, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U_{\lambda }=U_{0}} and $\lambda =1$, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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}}

where

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} .