Quantum free energy differences from non-equilibrium path integrals: II. Convergence properties for the harmonic oscillator
arXiv:0807.0409 · doi:10.1103/PhysRevE.78.041104
Abstract
Non-equilibrium path integral methods for computing quantum free energy differences are applied to a quantum particle trapped in a harmonic well of uniformly changing strength with the purpose of establishing the convergence properties of the work distribution and free energy as the number of degrees of freedom M in the regularized path integrals goes to infinity. The work distribution is found to converge when M tends to infinity regardless of the switching speed, leading to finite results for the free energy difference when the Jarzynski non-equilibrium work relation or the Crooks fluctuation relation are used. The nature of the convergence depends on the regularization method. For the Fourier method, the convergence of the free energy difference and work distribution go as 1/M, while both quantities converge as 1/M^2 when the bead regularization procedure is used. The implications of these results to more general systems are discussed.
26 pages, 6 figures. Added clarifying remarks and fixed typos
References in corpus (12)
- A nonequilibrium equality for free energy differences
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
- Fluctuation theorems: Work is not an observable
- Nonequilibrium work distribution of a quantum harmonic oscillator
- Fluctuation theorems for quantum master equations
- Optimized Verlet-like algorithms for molecular dynamics simulations
- A quantum version of free energy - irreversible work relations
- Microcanonical quantum fluctuation theorems
- Optimized Forest-Ruth- and Suzuki-like algorithms for integration of motion in many-body systems
- Quantum free energy differences from non-equilibrium path integrals: I. Methods and numerical application
- Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion
Cited by in corpus (11)
- Quantum work statistics of linear and nonlinear parametric oscillators
- Quantum mechanics of open systems: Dissipaton theories
- Interference of Identical Particles and the Quantum Work Distribution
- Equilibrium and transient thermodynamics: A unified dissipaton-space approach
- Quantum free energy differences from non-equilibrium path integrals: I. Methods and numerical application
- Nonequilibrium Quantum Free Energy and Effective Temperature, Generating Functional and Influence Action
- Jarzynski equality for conditional stochastic work
- Quantum Work Fluctuations in connection with Jarzynski Equality
- Thermalization processes induced by quantum monitoring in multi-level systems
- Theoretical formulations on thermodynamics of quantum impurity systems
- Calculation of semiclassical free energy differences along non-equilibrium classical trajectories