Calculating the free energy difference by applying the Jarzynski equality to a virtual integrable system
arXiv:1805.10064 · doi:10.1103/PhysRevE.98.022117
Abstract
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 the FED of a system may be facilitated by considering instead another virtual system designed to this end. Taking advantage of this flexibility and the JE, we show that by introducing an integrable virtual system, the evolution problem involved in the JE can be solved. As a consequence, FED is expressed in the form of an equilibrium equality, in contrast with the nonequilibrium JE it is based on. Numerically, this result allows FED to be computed by sampling the canonical ensemble directly and the computational cost can be significantly reduced. The effectiveness and efficiency of this scheme are illustrated with numerical studies of several representative model systems.
arXiv comment10 pages, 9 figures
References in corpus (16)
- A nonequilibrium equality for free energy differences
- Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
- Optimal finite-time processes in stochastic thermodynamics
- Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
- Rare events and the convergence of exponentially averaged work values
- An experimental test of the Jarzynski equality in a mechanical experiment
- Simulating rare events in dynamical processes
- Heat conduction in the diatomic Toda lattice revisited
- Boosting work characteristics and overall heat engine performance via shortcuts to adiabaticity: quantum and classical systems
- Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation
- Targeted free energy perturbation
- On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example
- Single-ensemble nonequilibrium path-sampling estimates of free energy differences
- Equilibrium free energies from fast-switching trajectories with large time steps
- Non-integrability and the Fourier heat conduction law
- Suppression of work fluctuations by optimal control: An approach based on Jarzynski's equality