Uma derivação e quantificação geral da Terceira Lei da Termodinâmica

segunda-feira, março 27, 2017

A general derivation and quantification of the third law of thermodynamics

Lluís Masanes & Jonathan Oppenheim

Nature Communications 8, Article number: 14538 (2017)

Quantum information Thermodynamics

Received: 31 March 2016 Accepted: 09 January 2017 Published online: 14 March 2017


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.


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


Department of Physics & Astronomy, University College of London, London WC1E 6BT, UK

Lluís Masanes & Jonathan Oppenheim


All authors have contributed extensively to the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Lluís Masanes.