Negative Pressures in Classical and Cosmological Fluids and Their Thermodynamic Stability

The purpose of this paper is to establish reasonable limits to negative pressures in classical and cosmological fluids based on well-known present physical theories and discuss their thermodynamic stability. We begin the paper deriving the well-known equation of state of an ideal gas from thermodynamics and kinetic theory, using the equipartition of energy. Both non-relativistic and relativistic cases are discussed. From the results it is clear that for an ideal gas pressure can only be positive and proportional to the density (of mass or energy). In order to discuss a system where pressure can be negative we review the van der Waals fluid, which presents negative pressure only in liquid metastable states. Then we present the requirements that should be fulfilled by a Chaplygin type fluid; where pressure is negative and goes with a negative power of the energy density, in order to satisfy thermodynamical conditions of stability. Finally we consider the equation of state P = -B rho (B > 0) and show that it satisfies the conditions of stability but violates the third law of thermodynamics. Besides that, the temperature of this fluid increases during an adiabatic expansion.