  Dissipaton-equation-of-motion (DEOM) theory [Y. J. Yan, J. Chem. Phys. 140,
054105 (2014)] is an exact and nonperturbative many-particle method for open
quantum systems. The existing dissipaton algebra treats also the dynamics of
hybrid bath solvation coordinates. The dynamics of conjugate momentums remain
to be addressed within the DEOM framework. In this work, we establish this
missing ingredient, the dissipaton algebra on solvation momentums, with
rigorous validations against necessary and sufficient criteria. The resulted
phase-space DEOM theory will serve as a solid ground for further developments
of various practical methods toward a broad range of applications. We
illustrate this novel dissipaton algebra with the phase-space DEOM-evaluation
on heat current fluctuation.
