Editing 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 <math>U_\lambda</math> such that
<math>\lambda=0</math>,  <math>U_\lambda=U_0</math>
and
<math>\lambda=1</math>, <math>U_\lambda=U</math>

<math>\Delta A = A - A_0 = \int_0^1 d\lambda  <\frac{\partial U_\lambda}{\partial \lambda}>_{\lambda}</math>


<math>U_\lambda=(1-\lambda)U_0 + \lambda U</math>