Resolution of a Classical Gravitational Second-Law Paradox

Sheehan and coworkers have claimed [D. P. Sheehan et al., Found. Phys. 30, 1227 (2000); 32, 441 (2002); D. P. Sheehan, in Quantum Limits to the Second Law, AIP Conference Proceedings 643 (American Institute of Physics, Melville, NY, 2002), p. 391] that a dilute gas trapped between an external shell and a gravitator can support a steady state in which energy flux by particles in one direction is balanced by energy flux by radiation in the opposite direction, and in which work can be extracted from an isothermal heat reservoir, thereby violating the second law of thermodynamics. In this paper, we identify a fundamental error in their simulation and analysis of their model system that vitiates their conclusions. We analyze a simpler, exactly soluble, three-dimensional model of a very dilute gas in a gravitational field between two thermal reservoirs, and show that their conclusions are not supported for the simple model. We show that their method of simulation, when applied to either the simple model or their more complex model under simpler conditions where the answers are known, leads to unphysical results. We also show that, when appropriate sampling is done, their model gives results in accord with the second law and detailed balance.