Dissipative (ohmic friction coefficient 2λ) and thermal effects in the quantum tunnelling decay rate Γ(λ, T, ε) of a weakly biased (energy |ε|⪡Ub) metastable oscillator (frequency ω0, leaking into free space through a quartic potential energy barrier (height Ub), are found to depend on the dimensionless bias parameter E0≡(|ε|32Ub)exp(ℏω02kBT). The freezing phenomenon reported in paper II, i.e. Γ(λ≠0,T=0,ε=0) = 0 − while Γ(λ=0, T≠0, ε=0) = Γ0 equals the tunnelling rate for the isolated system discussed in paper I — , is shown to occur only at strictly zero bias (E0=0, even at T=0). Any ε≠0 implies E0=∞ at T=0, which leads to Γ(λ=0, T=0, ε≠0) = Γ0 independent of the oder in which the zero damping and zero temperature limits are taken.
