Abstract
A result of great theoretical and experimental interest, the Jarzynski equality predicts a free energy change of a system at inverse temperature from an ensemble average of nonequilibrium exponential work, i.e., . The number of experimental work values needed to reach a given accuracy of is determined by the variance of , denoted . We discover in this work that in both harmonic and anharmonic Hamiltonian systems can systematically diverge in nonadiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence. This divergence may be regarded as a type of dynamically induced phase transition in work fluctuations. For a quantum harmonic oscillator with time-dependent trapping frequency as a working example, any nonadiabatic work protocol is found to yield a diverging at sufficiently low temperatures, markedly different from the classical behavior. The divergence of indicates the too-far-from-equilibrium nature of a nonadiabatic work protocol and makes it compulsory to apply designed control fields to suppress the quantum work fluctuations in order to test the Jarzynski equality.
- Received 6 February 2017
- Revised 24 September 2017
DOI:https://doi.org/10.1103/PhysRevE.96.042119
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