The basic principles that govern nonequilibrium behaviors in materials have often been elusive. There was little such problem in solidification theory, where accepted theories of heat transfer and phase transitions automatically were consistent with the laws of thermodynamics. Thus, developments starting from the Mullins-Sekerka instability, through understanding the singular role played by surface tension, and the invention of phase-field methods, did not generate much controversy. With the advent of powerful computers, and with the leadership of Rappaz and others, numerical simulation has become one of our most powerful tools for research in solidification processing. The situation is entirely different in solid mechanics, where leaders of the field have insisted that only phenomenological strategies are feasible, and that statistical concepts such as entropy are not useful. Recently, however, there have been some promising counter-developments, including new statistical ideas, and even a calculation of fracture toughness using an analog of phase-field methods.