Negative thermodynamic pressure: no-go theorem and yes-go examples

Theory and experiment have long discussed negative thermodynamic pressure states, but their microscopic origins are unclear. I address this problem within the framework of quantum thermodynamics. I show that the pressure exerted on the boundary is positive when there is no interaction with the boundary. This is formalized by a no-go theorem that holds for any quantum state with finite motion. As a consequence of this analysis, I deduce a general formula for quantum non-equilibrium pressure. It is believed that stable negative pressure states cannot exist in gases. I provide solvable examples of quantum and classical gases, where negative pressure is achieved due to a suitable coupling with the boundary walls.