Thermodynamic integration method

The aim of thermodynamic integration is to compute the difference in a thermodynamic property (usually the free energy) of the system between some reference state and the state of interest. To measure the free energy change from initial to final state, thermodynamic parameters characterizing the system are changed infinitely slowly so that at each stage along the path the system is in equilibrium. This ensures that the path is reversible, i.e., the same path can be traversed in the opposite direction. In an experimental set-up, we are limited to a few thermodynamic variables such as volume, pressure, temperature in order to control the path. In a molecular simulation experiment, however, in addition to thermodynamic parameters, one can also change the interaction potential of the system and introduce suitable external potentials, making it possible to have a large variety of reversible paths and reference states [1]. In many simulation experiments, one measures the work required to change a single parameter (say λ) that characterizes the path. If the path is reversible, work measured is equal to change in the appropriate free energy. This is seen from the following derivation [2]: