title: Relative thermalization.
abstract: Locally thermal quantum systems may contradict traditional thermodynamics: heat can flow from a cold body to a hotter one, if the two are highly entangled. We show that to recover thermodynamic laws, we must use a stronger notion of thermalization: a system S is thermal relative to a reference R if S is both locally thermal and uncorrelated with R. Considering a general quantum reference is particularly relevant for a thermodynamic treatment of nanoscale quantum systems. We derive a technical condition for relative thermalization in terms of conditional entropies. Established results on local thermalization, which implicitly assume a classical reference, follow as special cases.
authors.affiliation: School of Physics, University of Bristol, BS8 1TL Bristol, United Kingdom.|Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.
authors.forename: Lídia
authors.initials: L
authors.lastname: Del Rio
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.|Department of Physics, University of Basel, 4056 Basel, Switzerland.|Centre for Quantum Technologies, National University of Singapore, 117543 Singapore.
authors.forename: Adrian
authors.initials: A
authors.lastname: Hutter
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.
authors.forename: Renato
authors.initials: R
authors.lastname: Renner
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 117543 Singapore.|QuTech, Delft University of Technology, 2628 CJ Delft, The Netherlands.
authors.forename: Stephanie
authors.initials: S
authors.lastname: Wehner