Cotunneling effects in the geometric statistics of a nonequilibrium spintronic junction

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.