TY - JOUR

T1 - Third law of thermodynamics as a single inequality

AU - Wilming, Henrik

AU - Gallego, Rodrigo

N1 - Funding Information: We thank Lluis Masanes, Joseph M. Renes, and Jens Eisert for interesting discussions and valuable feedback. This work has been supported by the European Research Council (ERC) (TAQ), the Deutsche Forschungsgemeinschaft (DFG) (GA 2184/2-1), and the Studienstiftung des Deutschen Volkes.

PY - 2017/11/13

Y1 - 2017/11/13

N2 - The third law of thermodynamics in the form of the unattainability principle states that exact ground-state cooling requires infinite resources. Here, we investigate the amount of nonequilibrium resources needed for approximate cooling.We consider as a resource any system out of equilibrium, allowing for resources beyond the independent and identically distributed assumption and including the input of work as a particular case. We establish in full generality a sufficient and a necessary condition for cooling and showthat, for a vast class of nonequilibrium resources, these two conditions coincide, providing a single necessary and sufficient criterion. Such conditions are expressed in terms of a single function playing a role for the third law similar to the one of the free energy for the second law. From a technical point of view, we provide newresults about the concavity or convexity of certain Renyi divergences, which might be of independent interest.

AB - The third law of thermodynamics in the form of the unattainability principle states that exact ground-state cooling requires infinite resources. Here, we investigate the amount of nonequilibrium resources needed for approximate cooling.We consider as a resource any system out of equilibrium, allowing for resources beyond the independent and identically distributed assumption and including the input of work as a particular case. We establish in full generality a sufficient and a necessary condition for cooling and showthat, for a vast class of nonequilibrium resources, these two conditions coincide, providing a single necessary and sufficient criterion. Such conditions are expressed in terms of a single function playing a role for the third law similar to the one of the free energy for the second law. From a technical point of view, we provide newresults about the concavity or convexity of certain Renyi divergences, which might be of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=85034449335&partnerID=8YFLogxK

U2 - 10.1103/PhysRevX.7.041033

DO - 10.1103/PhysRevX.7.041033

M3 - Article

AN - SCOPUS:85034449335

VL - 7

JO - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 4

M1 - 041033

ER -