Entropy (S) quantifies the total heat required to bring the quantum state of molecular systems from absolute zero to a given temperature (TS). Our recent paper has shown that the entropy of atmospheric gases is a simple logarithmic sum function of the vibrational, rotational and translational action, defined as @ equals mrv (Kennedy et al 2019 Entropy  21,454). For example, translational entropy of atmospheric gases can be expressed as

S_t = Rln[e^2.5(2πmkT)^1.5V/h³N] = Rln[e^2.5(3kTI/ħ³z_t] = Rln[e^2.5(@_t/ħ)³]

Here, z_t corrects Maxwell’s rms velocity to mean molecular velocity (v_t) and r_t  is half the mean separation. The principle of least action suggests inclusion of a fourth degree of freedom that must also absorb heat, that of the vortical action expressed as large scale molecular interaction in anticyclones and cyclones. Vortical action (@_vor = ΣmR²Ω, 1-dimensional) would significantly increase the heat capacity as a function of work performed in developing its angular momentum, without increase in temperature. This increased heat capacity similar to a mechanical fly-wheel effect would be a negative feedback to changes in temperature and climate sensitivity from greenhouse forcing. Furthermore, it should provide a cause of surface warming from dissipative vorticity and resultant turbulent processes in the boundary of the troposphere up to 2 km, a function of surface roughness. The hypothesis of vortical action and entropy and its dissipation significant for surface warming as downwelling radiation, climate sensitivity and climate modelling will be discussed in the context of possible tests to refute or support this hypothesis.      

∑S=    ∑S_{(vibrational + rotational + translational + vortical)}