A general derivation and quantification of the third law of thermodynamics
Lluís Masanes & Jonathan Oppenheim
Nature Communications 8, Article number: 14538 (2017)
doi: 10.1038/ncomms14538
Quantum information Thermodynamics
Received: 31 March 2016 Accepted: 09 January 2017 Published online: 14 March 2017
Abstract
The most accepted version of the third law of thermodynamics, the unattainability principle, states that any process cannot reach absolute zero temperature in a finite number of steps and within a finite time. Here, we provide a derivation of the principle that applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any temperature, and translate these resources into the minimal time or number of steps, by considering the notion of a thermal machine that obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our results also clarify the connection between two versions of the third law (the unattainability principle and the heat theorem), and place ultimate bounds on the speed at which information can be erased.
Acknowledgements
We are grateful for discussions with Jacob Bekenstein, Fernando Brandao, Karen Hovhannisyan, Ronnie Kosloff, Michał Horodecki, Pawel Horodecki and Mischa Woods. L.M. is supported by the EPSRC, and J.O. is supported by EPSRC and by the Royal Society.
Author information
Affiliations
Department of Physics & Astronomy, University College of London, London WC1E 6BT, UK
Lluís Masanes & Jonathan Oppenheim
Contributions
All authors have contributed extensively to the paper.
Competing interests
The authors declare no competing financial interests.
Corresponding author
Correspondence to Lluís Masanes.
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