The second laws of quantum thermodynamics

@article{Brando2015TheSL,
  title={The second laws of quantum thermodynamics},
  author={Fernando G. S. L. Brand{\~a}o and Michal Horodecki and Nelly Huei Ying Ng and Jonathan Oppenheim and Stephanie Wehner},
  journal={Proceedings of the National Academy of Sciences},
  year={2015},
  volume={112},
  pages={3275 - 3279}
}
Significance In ordinary thermodynamics, transitions are governed by a single quantity–the free energy. Its monotonicity is a formulation of the second law. Here, we find that the second law for microscopic or highly correlated systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on state transformations, but many. We find a family of quantum free energies which generalize the standard free energy, and can never increase. The ordinary… 

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References

SHOWING 1-10 OF 64 REFERENCES

Fundamental limitations for quantum and nanoscale thermodynamics.

TLDR
It is found that there are fundamental limitations on work extraction from non-equilibrium states, owing to finite size effects and quantum coherences, which implies that thermodynamical transitions are generically irreversible at this scale.

N ov 2 01 1 Fundamental limitations for quantum and nano thermodynamics

The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit – when the number of particles involved becomes very large. Here we study thermodynamics in the

Resource theory of quantum states out of thermal equilibrium.

TLDR
It is shown that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sub linear amount of classical communication required for entanglement dilution.

Extracting work from quantum systems

We consider the task of extracting work from quantum systems in the resource theory perspective of thermodynamics, where free states are arbitrary thermal states, and allowed operations are energy

Extraction of work from a single thermal bath in the quantum regime

TLDR
It is shown that then work can be extracted from the bath by cyclic variation of a parameter, and thermodynamic relations are shown to take a generalized Gibbsian form that may violate the Clausius inequality.

The thermodynamics of computation—a review

Computers may be thought of as engines for transforming free energy into waste heat and mathematical work. Existing electronic computers dissipate energy vastly in excess of the mean thermal

A framework for non-asymptotic quantum information theory

TLDR
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography, and introduces the purified distance, a novel metric for unnormalized quantum states, and explores various properties of these entropies, including data-processing inequalities, chain rules and their classical limits.

Thermodynamic Cost of Reliability and Low Temperatures: Tightening Landauer's Principle and the Second Law

TLDR
A general framework describing the “thermodynamic worth” of the resources with respect to reliable bit erasure or good cooling is developed, which turns out to be given by the distinguishability of the resource's state from its equilibrium state in the sense of a statistical inference problem.

Quantum f-divergences and error correction

TLDR
It is shown that the quantum f-divergences are monotonic under the dual of Schwarz maps whenever the defining function is operator convex, and an integral representation for operator conveX functions on the positive half-line is provided, which is the main ingredient in extending previously known results on the monotonicity inequality and the case of equality.
...