Stable singular or negative stiffness systems in the presence of energy flux

We report stable systems which exhibit quasistatic stiffness that can be negative or tend to infinity without external constraint. They are based on coupled fields in the non-equilibrium presence of energy flux that is modulated by force. They evade thermodynamic restrictions by relaxing a restrictive assumption: equilibrium. Negative values of physical properties, including compressibility and heat capacity, are considered forbidden in classical thermodynamics; such analyses provide bounds on the stiffness and other properties of multiphase materials. Stable negative and singular stiffness is demonstrated experimentally in a piezoelectric system and in a thermoelastic granular material. Coupled fields occur naturally under a wide range of conditions and form the basis for many forms of technology including sensors, actuators, and electric coolers. Because all materials exhibit at least one coupled field effect, the concept is broadly general and is applicable to attaining extreme values of any physical property e.g. stiffness, permittivity, piezoelectricity.