Equilibration to the non-Abelian squeezed-thermal reservoir with three charges

In quantum thermodynamics, the noncommutativity of conserved quantities is a key aspect of generalized reservoirs. Squeezed-thermal reservoirs, characterized as non-Abelian thermal reservoirs with noncommuting constant quantities (charges), are redefined in this study using SU(1,1) Lie algebra generators. Our findings suggest that these reservoirs can be more accurately described as generalized Gibbs ensembles featuring three noncommuting operators instead of the generally assumed two. By incorporating three charges and the quantum phase-space method to describe dissipation into such a reservoir, two expressions for Wigner entropy production are derived: one based on the stationary mean value of the exchanged charges and another based on a single operator's stationary mean value---the Casimir operator of the Lie algebra. Analysis of these expressions across two distinct models sheds light on equilibration conditions with generalized reservoirs during the interconversion of noncommuting charges.