Definition and measurement of work done on a driven quantum
system remains a major challenge in quantum thermodynamics.
For closed systems, the standard way to define work is to
consider the two-measurement protocol (TMP), where the
system is measured at the beginning and end of the drive
leading to wave function collapse (loss of quantum
coherence) to an energy eigenstate. For open systems, the
stochastic mapping to the Lindblad master equation and its
unraveling by quantum jumps offers a powerful way to define
and calculate thermodynamics of work and the related
fluctuation relations within the TMP .
However, for quantum systems with coherence it has recently
been shown that it is impossible to define a work operator
that satisfies proper physical requirements (the "no-go"
theorem) . To this end, we propose a novel way to define
work based on the Hamilton-Jacobi formulation of quantum
mechanics, which allows to define phase space trajectories
with well-defined energy for any wave function . We
illustrate this approach by explicit calculations for a
driven quantum harmonic oscillator.
1. S. Suomela, J. Salmilehto, I.G. Savenko, T. Ala-Nissila,
and M. Mottonen, Phys. Rev. E 91, 022126 (2016).
2. M. Perarnau-Llobet, E. Baumer, K.V. Hovhannisyan, M.
Huber, and A. Acin, Phys. Rev. Lett. 118, 070601 (2017).
3. R. Sampaio, S. Suomela, T. Ala-Nissila, J. Anders, and
Th. Philbin, https://arxiv.org/abs/1707.06159(2017).