Optimizing the switching function for nonequilibrium free-energy calculations: An on-the-fly approach

Abstract

Using nonequilibrium switching simulations to determine the free-energy difference between two thermodynamic states has gained tremendous popularity since Jarzynski's identity was proposed. The efficiency of a nonequilibrium switching simulation depends on the switching function. A well selected switching function can significantly minimize the associated dissipative work and reduce the computational cost of nonequilibrium free-energy simulations. In this paper, a method for estimating an efficient switching function during a nonequilibrium free-energy simulation is presented. The switching rate depends on the fluctuation of the fictitious force and a relaxation time. This method is similar to a prior method described by de Koning [J. Chem. Phys. 122, 104106 (2005)], except in our approach the switching rate is determined on-the-fly without the need for trial pulls. Our method can be easily incorporated into any existing implementation of the nonequilibrium switching method. The on-the-fly approach was used to determine the transformation free energy between two types of Einstein crystals and the isothermal free energy of expansion of a van der Waals gas. For both of the test cases, our on-the-fly method is found to provide a switching function much more superior than the standard one.

Degenerate optimal paths in thermally isolated systems

“…The next step is to calculate the constant C. From Eqs. (9) and (14), we obtain C = 2/(4β 2 λ 2 0 ). Finally, the relaxation function reads…”

“…In this situation, the minimal energetic cost is equal to the difference of Helmholtz free energies. Thereby, one of the many applications of such optimal finite-time processes is the estimation of free-energy differences [5][6][7][8][9][10]. A major breakthrough in this problem was achieved by Jarzynski [11] and Crooks [12].…”

Stochastic thermodynamics, fluctuation theorems and molecular machines

“…An important line of research in this context is to find methods for dealing with the error caused by having only finite (and even noisy) data for evaluating the nonlinear averages involved in the JR and the HSR. Some of the papers dealing with this issue are [86,137,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480].…”

Optimal driving of isothermal processes close to equilibrium

“…Then we ask for the optimal protocol λ * t that drives the system from H(λ 0 ) to H(λ τ ) such that the least amount of work is dissipated during finite time τ . In previous works this question has been addressed within two independent approaches: If full information about the microscopic properties of the system is available the dynamics can be described by a Langevin equation [24][25][26][27] , whereas phenomenological treatments rely on methods of linear response theory [28][29][30][31] . Generally, solutions obtained within the microscopic treatment are exact and valid for any kind of driving, fast and slow, strong and weak, whereas phenomenological treatments have been restricted to weak, slow driving.…”