Passivity, complete passivity, and virtual temperatures

Paul Skrzypczyk, Ralph Silva, Nicolas Brunner

Research output: Contribution to journalArticle (Academic Journal)peer-review

43 Citations (Scopus)


We give a simple and intuitive proof that the only states which are completely passive, i.e., those states from which work cannot be extracted even with infinitely many copies, are Gibbs states at positive temperatures. The proof makes use of the idea of virtual temperatures, i.e., the association of temperatures to pairs of energy levels (transitions). We show that (1) passive states are those where every transition is at a positive temperature and (2) completely passive states are those where every transition is at the same positive temperature.

Original languageEnglish
Article number052133
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - 19 May 2015


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