TY - JOUR
T1 - Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
AU - Yunger Halpern, Nicole
AU - Faist, Philippe
AU - Oppenheim, Jonathan
AU - Winter, Andreas
PY - 2016/7/7
Y1 - 2016/7/7
N2 - © 2016 The Author(s). 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.
AB - © 2016 The Author(s). 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.
U2 - 10.1038/ncomms12051
DO - 10.1038/ncomms12051
M3 - Article
VL - 7
JO - Nature Communications
JF - Nature Communications
SN - 2041-1723
M1 - 12051
ER -