Two centuries after Carnot defined thermodynamics as a scientific discipline based on work by engineers like James Watt, can we learn more from Carnot’s perceptive analysis of maximum power from heat engines? Using action mechanics, the rate of work in Carnot’s heat engine cycle can be integrated as external pressure-volume work, sustained by internal quantum field work, equal to changes in Gibbs free energy that was called caloric by Carnot. His treatise of 1824 even gave equations that express the work potential as a function of temperature and the logarithm of the change in volume. To answer this question, we apply Carnot’s principle defined by Clausius as entropy, to atmospheric heat-work cycles, such as in anticyclones. We show using Lagrange’s virial theorem how Carnot’s thermodynamic states as Gibbs potential become entangled with gravitational potential states. The effective capacitance of greenhouse gases for energy in the troposphere enable recycling of heat emitted from the Earth’s hot surface, thermally setting tropospheric air masses in action. By delaying irreversible emission of long wavelength quanta to space, this recycling process extends the residence time of solar energy in the troposphere as work, maximising troposphere entropy to the tropopause. The virial theorems of Lagrange and Clausius, governed on the principle of least action, provide a more accurate lapse rate in temperature with temperature in the atmosphere, replacing the paradigm of adiabatic expansion. Reversible 4-stage Carnot cycles, based on Lagrangian least variation in action, raise surface temperature and pressure from turbulent heat release, sustaining the weight of the atmosphere. New lessons for understanding climate dynamics are emerging from this virial-action analysis.