A new microscopic look into pressure fields and local buoyancy

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Defining local pressures is pivotal to understanding phenomena such as buoyancy and atmospheric physics, which always require space-varying pressure fields to be considered. Such fields have precise definitions within the frameworks of hydro-thermodynamics and the kinetic theory of gases, but a pedagogical approach based on standard statistical mechanics techniques is still lacking. In this paper, we propose a new microscopic definition of local pressure inside a classical fluid, relying upon a local barometer potential that is built into the many-particle Hamiltonian. This setup allows pressure to be locally defined as an ensemble average of the radial force exerted by the barometer potential on the gas' particles. Moreover, this same framework is also employed in a microscopic derivation of buoyancy of immersed bodies in the presence of arbitrary external fields. As instructive examples, buoyant forces are calculated for ideal fluids in the presence of a uniform force field, in the presence of a spherical harmonic confinement field and in rotation with a constant angular velocity.