Does a Sponge Violate the Conservation of Energy?

Synopsis

When the volume of materials decreases under applied pressure it is said to have a positive compressibility. A material with negative compressibility (volume increases with an increase in pressure) seems to violate the conservation of energy, since it seems that a passive material, that contains no additional energy, is doing work on its environment. I'm going to talk about a recent paper [1], where a new structural design is proposed, which would have a negative compressibility if we substitute the actual volume with effective volume. Effective volume is the apparent bulk volume, which can be a mixture of solid and the gas from environment, like a sponge. With an increase in the pressure the structure expands and lets more air inside, that results in an increase in the effective volume. This expansion does not violate the energy conservation law since the actual work done is negative and the volume of the solid has decrease as usual. There are many important applications for such a material ranging from acoustic technologies to technology that work in places with extreme pressures like in space or deep in the ocean.

References:

[1] J. Qu, A. Gerber, F. Mayer, M. Kadic, and M. Wegener, Phys. Rev. X 7, 041060 (2017).