Cumulative work integrals contributions of the gas pressure associated with mode 1 (top panel) and mode 2 (bottom panel), starting from the bottom of the simulation, as a function of the logarithm of temperature. The total mode damping of each mode is used to normalize the work integrals. We note that due to boundary condition effects, the upper-most layers (log T <  3.64) must be considered with care (see text for details).