Traveling Phase Boundaries with the Broken Symmetries of Life

Living systems are the most important and most complex of nonequilibrium liquid crystalline systems. We check an experimental minimal model for macroscopic implications of this statement. To do this, we consider “living systems” in terms of three broken symmetries: 1. liquid crystalline (broken continuous symmetry); 2. chiral (broken mirror symmetry) and 3. non-equilibrium (broken time reversal symmetry). We call these three elements the Broken Symmetries of Life . The surprising result is that a model system with just these three elements, also “knows time”. The minimal model system is the traveling cholesteric liquid crystalisotropic liquid phase boundary prepared so that the length scale imposed on it by non-equilibrium driving forces is comparable to its equilibrium length, its pitch. In a pattern formation context, “knows time” means that a frequency is associated with all the patterns of this traveling interface. With the same non-equilibrium driving forces, its non-chiral analogue, the traveling nematic-isotropic liquid phase boundary, does not. Another surprise is our minimal model’s novel route to turbulence. Its non-chiral analogue prepared under identical conditions has no routes to turbulence. In contrast, as it was driven further from equilibrium, our minimal model’s repertoire ranges from a cellular pattern with a single wavelength and frequency, through a wavelength doubling breathing mode, followed by a phase winding flat interface that eventually becomes turbulent. To honor Professor Heppke’s long interest in and many contributions to the study of chiral liquid crystalline materials, phase diagrams and Life, this paper is a philosophical overview of our work on the traveling cholesteric (N*)-isotropic phase boundary [1,2].