Force from Equilibrium Fluctuation
(from classical to quantum and back!)
Pressure is a force from restriction of particle fluctuations
Force per unit area is a bulk property (function of equilibrium state)
independent of the shape of the container and potentials at the wall
independent of the dynamics of the particles (momentum integrations)
For a dilute gas:
(non-universal corrections)
Radiation: Photon density is temperature dependent:
Stefan-Boltzmann law of black-body pressure:
Casimir Force: Virtual photons (QED fluctuations) at low temperatures:
"On the attraction between two perfectly conducting plates," H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)
Quantum fluctuations of electromagnetic field in the vacuum between leads to an attractive force between perfect mirrors
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"The Theory of Molecular Attractive Forces Between Solids," E.M. Lifshitz, Soviet Physics 2, 73 (1956),
Generalizes above by considering fluctuating current sources in the bodies, and at finite temperatures.
Since 1995 confirmed in myriad experiments.
Lateral Casimir Force: A sideways
force to "align" corrugated plates into position of minimum energy:
"Mechanical Response of Vacuum," Golestanian, & Kardar, Phys. Rev. Lett. 78, 3421 (1997)
"Demonstration of the Lateral Casimir Force," F. Chen, U. Mohideen, et. al , Phys. Rev. Lett. 88, 101801 (2002)