The entropy per unit mass of moist air can be defined as
$$s=(1-q_t)(C_{pd} \ln{T}-R_d\ln{p_d})+q_tC_l\ln{T} + \frac{q_vL_v}{T}-q_vR_v\ln{\mathcal{H}}$$
And in statistical equilibrium, the entropy budget takes this following form
$$\frac{Q_{\mathrm{lat}}+Q_{\mathrm{sen}}}{T_{\mathrm{surf}}}+\frac{Q_{\mathrm{rad}}}{T_{\mathrm{rad}}}+\Delta{S}_{\mathrm{irr}}=0$$
These are all explained in this paper.
Irreversible entropy is produced from irreversible phase changes, the diffusion of water vapor, and the frictional dissipation of falling water vapor. Entropy can reduce the amount of work available to accelerate convective updrafts and downdrafts.
I'm just wondering - how will the amount of entropy in the atmosphere change as a result of climate change? Seeing that global warming tends to decrease the pole-to-equator gradient (resulting in a more homogeneous temperature distribution), I wonder if it might increase?
