---

The grand canonical ensemble lies at the core of quantum and classical  statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange  quantities represented by operators that fail to commute. Whether such  a ​ ​ system thermalizes and what form the thermal state has are questions  about ​ ​ truly quantum thermodynamics. Here we investigate this thermal  state from ​ ​ three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system- and-bath composite, tracing out the bath yields the system's thermal  state. This state is expected to be the equilibrium point, we argue,  of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity ​-- ​ the inability to extract work from equilibrium states ​ ​ -- ​, ​ implies  the thermal state's form, too. Our work opens new avenues into  equilibrium in the presence of quantum noncommutation. ​ [Based on arXiv:1512.01189]​

---

Andreas Winter, Universitat Autònoma de Barcelona
SR 0.03 TP
Contact: David Gross