  In the nonequilibrium steadystate of electronic transport across a
spin-resolved quantronic junction, we investigate the role of cotunneling on
the emergent statistics under phase-different adiabatic modulation of the
reservoirs' chemical potentials. By explicitly identifying the sequential and
inelastic cotunneling rates, we numerically evaluate the geometric or
Pancharatnam-Berry contributions to the spin exchange flux. We identify the
relevant conditions wherein the sequential and cotunneling processes compete
and selectively influence the total geometric flux upshot. The Fock space
coherences are found to suppress the cotunneling effects when the system
reservoir couplings are comparable. The cotunneling contribution to the total
geometric flux can be made comparable to the sequential contribution by
creating a rightsided asymmetry in the system-reservoir coupling strength.
Using a recently proposed geometric thermodynamic uncertainty relationship, we
numerically estimate the total rate of minimal entropy production. The
geometric flux and the minimum entropy are found to be nonlinear as a function
of the interaction energy of the junction's spin orbitals.
