Numerical verification of the generalized Crooks nonequilibrium work theorem for non-Hamiltonian molecular dynamics simulations

The generalized Crooks theorem (GCT) for deterministic non-Hamiltonian molecular dynamics simulations [Phys. Rev. E 75, 050101 (2007)] connects the probabilities of nonequilibrium realizations switching the system between two thermodynamic states, to the partition functions of these states. In comparison to the "classical" Crooks nonequilibrium work theorem [J. Stat. Phys. 90, 1481 (1998)], which deals with realizations involving only mechanical work, the GCT also accounts for additional work resulting from changes of the intensive and extensive thermodynamic variables of the system. In this article we present a numerical verification of the GCT using a Lennard-Jones fluid model where two particles are subject to a time-dependent external potential. Moreover, in order to switch the system between different thermodynamic states, the temperature and the pressure (or volume), which are controlled through the Martyna-Tobias-Klein equations of motion [J. Chem. Phys. 101, 4177 (1994)], are also varied externally. The free energy difference between states characterized by different distances of the target particles is evaluated using both a standard methodology (pair radial distribution functions) and the GCT. In order to exploit the various options provided by the GCT approach, i.e., the possibility of temperature/pressure/volume changes during the realizations, the free energy difference is recovered via arbitrary thermodynamic cycles. In all tests, the GCT is quantitatively verified.