Acoustic Casimir effect and fate of thermodynamics in mesoscopic matters

Abstract: 

Size effects become crucial for thermodynamics at low temperatures when the wavelength of thermal phonons becomes larger than the sample. We have observed such pushing phonons away in helium adsorbed on the nanotube. However, zero-point phonons remain, and we have demonstrated that the “vacuum” pressure depends greatly on the length, the so-called acoustic Casimir effect. With the increase of temperature, we have observed that thermal phonons enter first to longer samples while short samples remain in zero-point state. As pressure depends on the size, and energy becomes not additive anymore, usual thermodynamics fails to describe small matters. The size of the sample becomes the 4th independent variable in thermodynamic potential, in addition to P, T, and N. The additional coordinate promises to enrich the phase diagrams; for instance, quadruple points become formally possible.