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Colloquium: Materials that exceed classical thermodynamic bounds on properties

Roderic S. Lakes*

Roderic S. Lakes*

  • Department of Materials Science, Department of Engineering Physics, and Department of Mechanical Engineering University of Wisconsin, 1500 Engineering Drive, Madison, Wisconsin 53706-1687, USA

  • *Contact author: rlakes@wisc.edu
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Rev. Mod. Phys. 97, 021002 – Published 14 May, 2025

DOI: https://doi.org/10.1103/RevModPhys.97.021002

Abstract

Bounds on properties are useful in guiding design of heterogeneous materials and in understanding the distinction between effects that are physically reasonable and those that are not. Several bounds on physical properties can be exceeded by an appropriate choice of material. The reason is that the “proofs” of bounds contain either unstated assumptions about the material or assumptions that are couched in language that appears to be that of incontrovertible mathematics but that actually entails assumptions about the material. If those assumptions are relaxed, limits or bounds can be exceeded, as is demonstrated by analysis and experiments. For example, heat capacity, compressibility, electrical capacitance, and refractive index can be negative. Thermal expansion in composites can be larger or smaller than that of any constituent and can be negative. Materials and systems are known that are non-Hermitian or nonreciprocal. Currently, active fields of endeavor have arisen from such conceptual sources. Research efforts have led to the development of new materials and new classes of materials.

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Rev. Mod. Phys. 97, 021002– Published 14 May, 2025
  • Received 20 February 2024
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