title: Jarzynski matrix equality: Calculating the free-energy difference by nonequilibrium simulations with an arbitrary initial distribution.
abstract: The Jarzynski equality (JE) method, which relates the work of a nonequilibrium process to the free-energy difference between its initial and final states, provides an efficient way to calculate free energies of thermodynamic systems in simulations or experiments. However, more extensive applications of the JE are hindered by the requirement that the initial state must be in equilibrium. In this work we extend the JE method to be the Jarzynski matrix equality (JME) method, which relates the work of trajectories connecting metastable conformational regions to their local free energies, and thus we can estimate the free energy from the nonequilibrium trajectories starting from an almost arbitrary initial distribution. We then apply the JME to toy models, Lennard-Jones fluids, and polymer chain models, demonstrating its efficiency in free-energy calculations with satisfactory accuracy. The JME extends the applicability of the nonequilibrium methods to complex systems whose initial equilibrium states are difficult to reach.
authors.affiliation: School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
authors.forename: Biao
authors.initials: B
authors.lastname: Wan
authors.affiliation: School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
authors.forename: Cheng
authors.initials: C
authors.lastname: Yang
authors.affiliation: State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Yanting
authors.initials: Y
authors.lastname: Wang
authors.affiliation: School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
authors.forename: Xin
authors.initials: X
authors.lastname: Zhou