Figure 2
Equipartition and the equation of state. (a) The total energy of the system \(E\) normalized by \(k_{B}^{*} T\) as a function of swarm size (blue) along with the kinetic energy \(E_{k}\) (yellow) and potential energy \(E_{p}\) (blue). The total normalized energy of the system is well approximated by (9/2)N (black dashed line), indicating that each individual midge contributes \((9/2)k_{B}^{*} T\) to E and thus has 9 degrees of freedom (6 after discounting the factor of \({\text{ln}}2\) in our definition of \(k_{B}^{*} T\)). The deviations from that behaviour for the largest swarms can be attributed to a growing uncertainty in the energy due to the smaller number of experiments with such large swarms. (b) A portion of our ensemble of data of the measured pressure (blue). The yellow line is the reconstruction of the pressure from our equation of state. The inset shows a zoomed-in portion of the data to highlight the quality of the reconstruction. (c) PDF of the pressure for our entire data ensemble23. The statistics of the directly measured pressure (blue) and reconstructed pressure from the equation of state have nearly identical statistics for the full dynamic range of the signal.
