Optimizing the driving function for nonequilibrium free-energy calculations in the linear regime: A variational approach

de Koning, Maurice
March 2005
Journal of Chemical Physics;3/8/2005, Vol. 122 Issue 10, p104106
Academic Journal
We consider the issue of optimizing linear-regime nonequilibrium simulations to estimate free-energy differences. In particular, we focus on the problem of finding the best-possible driving function λ(t) that, for a given thermodynamic path, simulation algorithm, and amount of computational effort, minimizes dissipation. From the fluctuation-dissipation theorem it follows that, in the linear-response regime, the dissipation is controlled by the magnitude and characteristic correlation time of the equilibrium fluctuations in the driving force. As a result, the problem of finding the optimal switching scheme involves the solution of a standard problem in variational calculus: the minimization of a functional with respect to the switching function. In practice, the minimization involves solving the associated Euler–Lagrange equation subject to a set of boundary conditions. As a demonstration we apply the approach to the simple, yet illustrative problem of computing the free-energy difference between two classical harmonic oscillators with very different characteristic frequencies.


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