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

Abstract

We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in ${\hslash }^2$ 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 ${\hslash }^2$ 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.

References in corpus (16)

• A nonequilibrium equality for free energy differences
• Fluctuation theorems: Work is not an observable
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Fluctuation theorem for currents in open quantum systems
• Nonequilibrium work distribution of a quantum harmonic oscillator
• Fluctuation theorems for quantum master equations
• Comparison of free energy methods for molecular systems
• A quantum version of free energy - irreversible work relations
• Quantum work relations and response theory
• A Quantum Analogue of the Jarzynski Equality
• Unified Treatment of Quantum Fluctuation Theorem and Jarzynski Equality in Terms of microscopic reversibility
• Thermodynamics of a subensemble of a canonical ensemble
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems
• Quantum free energy differences from non-equilibrium path integrals: I. Methods and numerical application
• Quantum free energy differences from non-equilibrium path integrals: II. Convergence properties for the harmonic oscillator