  Memory formation in matter is a theme of broad intellectual relevance; it
sits at the interdisciplinary crossroads of physics, biology, chemistry, and
computer science. Memory connotes the ability to encode, access, and erase
signatures of past history in the state of a system. Once the system has
completely relaxed to thermal equilibrium, it is no longer able to recall
aspects of its evolution. Memory of initial conditions or previous training
protocols will be lost. Thus many forms of memory are intrinsically tied to
far-from-equilibrium behavior and to transient response to a perturbation. This
general behavior arises in diverse contexts in condensed matter physics and
materials: phase change memory, shape memory, echoes, memory effects in
glasses, return-point memory in disordered magnets, as well as related contexts
in computer science. Yet, as opposed to the situation in biology, there is
currently no common categorization and description of the memory behavior that
appears to be prevalent throughout condensed-matter systems. Here we focus on
material memories. We will describe the basic phenomenology of a few of the
known behaviors that can be understood as constituting a memory. We hope that
this will be a guide towards developing the unifying conceptual underpinnings
for a broad understanding of memory effects that appear in materials.
