How does pressure fluctuate in equilibrium

We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through the momentum current. We show that although the two expectation values converge to the same equilibrium value in the thermodynamic limit, the variance of the mechanical pressure is in general greater than that of the pressure defined through the thermodynamic relation. We also present a condition for experimentally detecting the difference between them in an idealized measurement of momentum transfer.