Thermodynamic length in open quantum systems

Matteo Scandi; Martí Perarnau-Llobet

doi:10.22331/q-2019-10-24-197

Thermodynamic length in open quantum systems

Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany

Published:	2019-10-24, volume 3, page 197
Eprint:	arXiv:1810.05583v5
Doi:	https://doi.org/10.22331/q-2019-10-24-197
Citation:	Quantum 3, 197 (2019).

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Abstract

The dissipation generated during a quasistatic thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocols correspond to geodesic trajectories. Here, we show how to generalize this approach to open quantum systems by finding the thermodynamic metric associated to a given Lindblad master equation. The obtained metric can be understood as a perturbation over the background geometry of equilibrium Gibbs states, which is induced by the Kubo-Mori-Bogoliubov (KMB) inner product. We illustrate this construction on two paradigmatic examples: an Ising chain and a two-level system interacting with a bosonic bath with different spectral densities.

Popular summary

Any thermodynamic protocol performed in finite time produces dissipation, and it is a crucial question how to minimise it. A particularly powerful approach to address this question is by means of differential geometry: one can associate a metric in the thermodynamic space in such a way geodesics correspond to minimally dissipative processes. In this paper we apply this idea (which started in the 80s for macroscopic systems) to open quantum systems described by a Lindblad equation, so that the problem of finding optimal thermodynamic protocols between two Hamiltonians reduces to the one of solving the geodesics equation. Differences with previous classical works appear in the presence of coherences in the energy basis, which are created when the Hamiltonian does not commute with itself at different times. We illustrate these ideas for a qubit coupled to a bath with different spectral densities, and an Ising chain in a controllable transverse field.

► BibTeX data

@article{Scandi2019thermodynamiclength,
  doi = {10.22331/q-2019-10-24-197},
  url = {https://doi.org/10.22331/q-2019-10-24-197},
  title = {Thermodynamic length in open quantum systems},
  author = {Scandi, Matteo and Perarnau-Llobet, Mart{\'{i}}},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {197},
  month = oct,
  year = {2019}
}

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[73] Elisa Bäumer, Martí Perarnau-Llobet, Philipp Kammerlander, Henrik Wilming, and Renato Renner. Imperfect Thermalizations Allow for Optimal Thermodynamic Processes. Quantum, 3: 153, June 2019. ISSN 2521-327X. 10.22331/q-2019-06-24-153. URL https://doi.org/10.22331/q-2019-06-24-153.
https://doi.org/10.22331/q-2019-06-24-153

[74] Roie Dann, Ander Tobalina, and Ronnie Kosloff. Shortcut to equilibration of an open quantum system. Phys. Rev. Lett., 122: 250402, Jun 2019. 10.1103/PhysRevLett.122.250402. URL https://link.aps.org/doi/10.1103/PhysRevLett.122.250402.
https://doi.org/10.1103/PhysRevLett.122.250402

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Thermodynamic length in open quantum systems

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