Free Energy Estimation in Dissipative Particle Dynamics

The methods for estimating the change of free energy in dissipative particle dynamics (DPD) are discussed on the basis of fluctuation theorems. Fluctuation theorems are tactics to evaluate free energy changes from non-equilibrium work distributions and have several forms, as proposed by Jarzynski, Crooks, and Bennett. The validity of these methods however, has been shown merely with the molecular dynamics or Langevin dynamics. In this study, the appropriate forms of fluctuation theorems for dissipative particle dynamics, which has similar structure to that of Langevin dynamics, are suggested using Liouville's theorem, and they are proved equivalent to original fluctuation theorems. Work distribution functions, which are probability distribution functions of works exerted on the system within the systematic change, are the basics of fluctuation theorems and their shapes are turned out to be dependent on the phase space trajectory of the change of the system. The reliability of Jarzynski and Crooks methods is highly dependent on the number of simulations to measure works and the shapes of the work distribution functions. Bennett method, however, can evaluate free energy changes even when Jarzynski and Crooks methods fail to do so.