<i>Colloquium</i>: Materials that exceed classical thermodynamic bounds on properties

Classical thermodynamic bounds provide constraints on values that are expected in measurements of certain physical properties. In a variety of fields, some measurements exceed these bounds. This apparent violation of thermodynamics arises because the measurements are made in ways that violate the underlying assumptions made when deriving these bounds. This Colloquium describes a wide variety of circumstances where such violations occur and which of the underlying assumptions are violated in each case. It also describes how interesting material properties can be developed using materials designed to violate these assumptions.