Demonstration of Jarzynski's Equality in Open Quantum Systems Using a Step-Wise Pulling Protocol

Abstract

We present a generalization of Jarzynski's Equality, applicable to quantum systems, relating discretized mechanical work and free-energy changes. The theory is based on a step-wise pulling protocol. We find that work distribution functions can be constructed from fluctuations of a reaction coordinate along a reaction pathway in the step-wise pulling protocol. We also propose two sets of equations to determine the two possible optimal pathways that provide the most significant contributions to free-energy changes. We find that the transitions along these most optimal pathways, satisfying both sets of equations, follow the principle of detailed balance. We then test the theory by explicitly computing the free-energy changes for a one-dimensional quantum harmonic oscillator. This approach suggests a feasible way of measuring the fluctuations to experimentally test Jarzynski's Equality in many-body systems, such as Bose-Einstein condensates.

9 pages, 5 figures

References in corpus (10)

• 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
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Superfluid and Dissipative Dynamics of a Bose-Einstein Condensate in a Periodic Optical Potential
• Nonequilibrium work distribution of a quantum harmonic oscillator
• Employing trapped cold ions to verify the quantum Jarzynski equality
• Quantum work relations and response theory
• A Parallel-pulling Protocol for Free-Energy Evaluation

Cited by in corpus (5)

• Measuring the characteristic function of the work distribution
• Assessing the non-equilibrium thermodynamics in a quenched quantum many-body system via single projective measurements
• Statistics of work done in degenerate parametric amplification process
• The distribution of work performed on a NIS junction
• Power of photonic states: from quantum computation to cosmology