"Quantum dissipation arising from quantum fluctuations and the quantum mechanics of macroscopic variables is important because of the ever decreasing size (mesoscale) of the nanoparticles used in technology. The most striking example occurs in information storage by magnetic nanoparticles, where the governing factor for magnetisation reversal by macroscopic quantum tunnelling is spin size S. The S dependence, with associated large quantum effects, becomes evermore marked as one proceeds from single domain particles to molecular clusters to single molecule magnets to individual spins. Here in the context of a general investigation of mesoscale quantum mechanics of particles (separable and additive Hamiltonians) and spins it is proposed to generalise Wigner’s quasi phase space formulation of quantum mechanics without dissipation (originally used to calculate quantum corrections to classical statistical mechanics i.e. the quantum/classical borderline characteristic of the mesoscale), to systems with non-separable Hamiltonians (spins) including the effects of dissipation to the surrounding heat bath. The results, obtained by (a) matrix continued fraction methods of solution of the appropriate master equations (b) computer simulation and (c) quantum Kramers escape rate theory will be compared with suitable experimental observations of the escape rate and the associated susceptibilities of nanoparticles."