(716g) Information Theory and the Thermodynamics of Irreversible Shape Changes

Irreversible shape change of a solid material requires the rearrangement of constituent building blocks into new positions. The change in uncertainty of these building block positions before and after the shape change operation can be construed as the change in the information content of the system. Information theory then helps us predict the minimum energetic cost of such an operation (given by Landauerâ??s principle). We apply this concept to the simple process of irreversible length change of an elastic solid under uniaxial tension and find that the minimum stress required to cause this deformation is given by k_BTln(2)/V*. Here k_B is the Boltzmann constant, T is the temperature and V* is the volume of a single, independently movable building block comprising the material. Interestingly, this stress closely predicts the experimentally calculated value for yield stress in a large variety of materials at room temperature. This suggests that the information loss during the irreversible shape change of an elastic material under tension significantly contributes to the energetic cost of this procedure. Looking closely at the microscale interactions between building blocks of the material, we observe that the positional uncertainty/information change is a result of a symmetry breaking when material flow occurs in one direction vs. the other along the line of action of the applied stress. We believe we have identified a new mechanism for energy dissipation in materials under mechanical stress undergoing irreversible shape change. The energy dissipated through this mechanism depends on the initial and final uncertainties in the material building block positions and is a function of temperature and the initial configuration of the system. This dissipation mechanism might hold the key to understanding the mechanics of biological active, adaptive materials as well as for the design of materials with autonomous shape transformation properties.