A general derivation and quantification of the third law of thermodynamics
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 infinitedimensional 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.
 Publication:

Nature Communications
 Pub Date:
 March 2017
 DOI:
 10.1038/ncomms14538
 arXiv:
 arXiv:1412.3828
 Bibcode:
 2017NatCo...814538M
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Substantial improvement of the third law derivation, which now only relies on a single assumption: the positivity of the heat capacity. 7 pages+appendix, 2 figures