The path to equilibrium is not controlled by entropy production. Although entropy increases with every time step, dynamical motion can be dominated by nonlinear physical process which spontaneously concentrate energy density. In sonoluminescence a bubble concentrates the energy of a traveling sound wave by 12 orders of magnitude to create picoseconds flashes of blackbody radiation that originate in a new state of matter. When surfaces are brought into and out of contact they exchange charge: a process call tribo-electrification. This phenomenon can be so strong that the power applied to peel sticky tape is efficiently transduced into a flux of high energy electrons, and x-ray photons that can expose an image in a few seconds. For a ferroelectric crystal, instabilities in the phonon spectrum lead to a spontaneous polarization that for Lithium Niobate reaches 15.million volts per cm. The temperature dependence of this field can be used to build a neutron generator based on the fusion of deuterium nuclei. These phenomena challenge a reductionist approach to the theoretical physics of emergent phenomena. The degree to which the energy density of a continuous system can be concentrated by off-equilibrium motion has not been determined by theory. For sonoluminescence we do not know if the parameter space includes a region where an extra factor of 100 in energy density makes it possible to realize thermonuclear fusion. For triboelectrification we do not have an ab-initio theory of charge transfer. And for ferroelectrics we do not have an ab-initio theory of the limits of spontaneous polarization which can be designed.