Equilibrium Pressure & Fluctuation-Induced Force

red ball Particles:  Pressure is a function of state.


yellow ball Force per unit area of the wall is a bulk property;

independent of the shape of the container and potentials at the wall

independent of the dynamics of the particles (momentum integrations)

yellow ball For a dilute gas:      (non-universal corrections)

red ball Radiation:  Photon density is temperature dependent:

Stefan-Boltzmann law of black-body pressure:

red ballCasimir Force: Virtual photons (QED fluctuations) at low temperatures:                    

yellow ball"On the attraction between two perfectly conducting plates," H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)

yellow ball Quantum fluctuations of electromagnetic field in the vacuum between leads to an attractive force between perfect mirrors


yellow ball"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.

yellow ball "Pressure" =>"Interaction"; Force per unit area of the wall is


Strongly dependent on the shape of the container

yellow ball Since 1995 confirmed in myriad experiments.

red ballParticles:  Thermal fluctuation-induced forces emerge when inter-particle forces lead to large correlation lengths.

is needed for long-range, as opposed to short-range "depletion" forces.)

yellow ballFinite-size corrections for free energy confined between plates take a universal form at criticality

M.E. Fisher and P.-G. de Gennes, C. R. Acad. Sci. Ser. B 287, 207 (1978)


Experimental confirmation of force in critical oil/water mixture. [measurement, lateral force]

Hertlein, Helden, Gambassi, Dietrich & Bechinger, Nature 451, 172 (2008)

Long-range correlations lead to long-range (universal) fluctuation-induced forces.

bluearrowGoldstone mode fluctuations following continuous symmetry breaking are long-range correlated

H. Li . Kardar, Phys. Rev. Lett. 67, 3275 (1991)

Experimental confirmation in wetting of superfluid films

yellow ballR. Garcia and M.H.W. Chan, Phys. Rev. Lett. 83, 1187 (1999)