Can the derivative defining pressure $dU \over dV$ or ${∂S \over ∂V}|_{E,N} $ be negative in processes occuring in system not cosmological but statistical (gases or solids or liquids - I mean the statistical study of systems). Altough I have read about negative temperatures and negative pressures, could we have for a system at positive temperature, a negative price of pressure (absolute)?
Note: I have read Are negative temperatures typically associated with negative absolute pressures?
Depending on how "real" you want the system to be. In a Casimir plate setup in a way the vacuum gets a negative pressure. But for any system of real particles a negative pressure means, that the system will be unstable and collapse, so you cannot have negative pressure in equilibrium. For example, negative pressure can formally occur in the van der Waals model of non-ideal gases, but there it is only an artifact as the uniform phase is unstable (even when the pressure does not drop below zero), and instead there is an equilibrium between gas and liquid at a constant temperature and pressure.
