Calculation of semiclassical free energy differences along non-equilibrium classical trajectories

TL;DR

This paper develops methods to compute semiclassical free energy differences along classical trajectories, incorporating quantum effects through temperature-dependent potential terms, enabling classical simulations to estimate quantum free energies.

Contribution

It introduces relations for evaluating quantum-corrected free energy changes using purely classical Hamiltonians with additional potential terms proportional to , applicable in molecular dynamics.

Findings

Derived relations for semiclassical free energy differences.

Formulated semiclassical partition functions using classical trajectories.

Discussed quantum interference effects on nonequilibrium work.

Abstract

We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in $\hbar^{2}$ along classically generated trajectories. The results are formulated in terms of purely classical Hamiltonians and trajectories, so that semiclassical partition functions can be computed, e.g., via classical molecular dynamics simulations. The Hamiltonians, however, contain additional potential-energy terms, which are proportional to $\hbar^{2}$ and are temperature-dependent. We discussed the influence of quantum interference on the nonequilibrium work and problems with unambiguous definition of the semiclassical work operator.