Theorie Kolloquium | June 30, 16:30

Grand canonical Gibbs state for systems with non-commuting charges

Andreas Winter

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]​


Universitat Autònoma de Barcelona
SR 0.03 TP
Contact: David Gross