title: 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 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.
authors.affiliation: Department of Physics &Astronomy, University College of London, London WC1E 6BT, UK.
authors.forename: Lluís
authors.initials: L
authors.lastname: Masanes
authors.affiliation: Department of Physics &Astronomy, University College of London, London WC1E 6BT, UK.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Oppenheim