Above the critical temperature of a real gas, if we compress it, to whatever extent, it doesn't get liquefied (no gas liquid interface). However, it does behave like liquids , esp. in case of very high pressures (upto 300 atm) it's physical properties are almost like liquids due to decreased intermolecular distance and increased intermolecular forces, yet is not a liquid but condensed vapors. Now , the Boltzmann distribution assumes negligible intermolecular forces so that the total energy of the system consists of only individual kinetic energies of the molecules, $E_{\text {total}} = \Sigma_i K_i$. So, in the aforementioned case of supercritical fluids, does the Boltzmann distribution still hold true, with only an increased number of energy states , including the intermolecular potential energies, i.e. $E_{\text {total}} = \Sigma_i K_i +\Sigma_{i≠j} V_{ij}$? Or will we have to search for another statistical distribution? Any help/suggestions please.
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