Recovering the Crooks equation for dynamical systems in the isothermal-isobaric ensemble: a strategy based on the equations of motion

The Crooks equation Eq. (10) in J. Stat. Phys. 90, 1481 (1998)] relates the work done on a system during a nonequilibrium transformation to the free energy difference between the final and the initial state of the transformation. Recently, the authors have derived the Crooks equation for systems in the canonical ensemble thermostatted by the Nose-Hoover or Nose-Hoover chain method P. Procacci et al., J. Chem. Phys. 125, 164101 (2006)]. That proof is essentially based on the fluctuation theorem by Evans and Searles Adv. Phys. 51, 1529 (2002)] and on the equations of motion. Following an analogous approach, the authors derive here the Crooks equation in the context of molecular dynamics simulations of systems in the isothermal-isobaric (NPT) ensemble, whose dynamics is regulated by the Martyna-Tobias-Klein algorithm J. Chem. Phys. 101, 4177 (1994)]. Their present derivation of the Crooks equation correlates to the demonstration of the Jarzynski identity for NPT systems recently proposed by Cuendet J. Chem. Phys. 125, 144109 (2006)].