Calculating the free energy difference by applying the Jarzynski equality to a virtual integrable system

Liyun Zhu, Jiao Wang

Published 2018-05-25Version 1

The Jarzynski equality (JE) provides a nonequilibrium method to measure and calculate the free energy difference (FED). Note that if two systems share the same Hamiltonian at two equilibrium states, respectively, they share the same FED between these two equilibrium states as well. Therefore the calculation of FED of a system may be facilitated by considering instead another virtual system designed to this end. Taking advantage of this flexibility and JE, we show that by introducing an integrable virtual system, the evolution problem involved in JE can be solved and as a consequence, FED is expressed in the form of an equilibrium equality. Numerically, this result allows FED to be computed by directly sampling the canonical ensemble and the computational cost can be significantly reduced. The effectiveness and efficiency of this scheme are illustrated with two one-dimensional (1D) models that represent 1D lattices and fluids, respectively.