Quasi-entropy and applications in liquid crystals

Angular moments are essential variables in various physical systems, including but not limited to liquid crystals. In many cases, we need an entropy term about these moments. One standard approach is to define it from the maximum entropy state, called the original entropy. But the resulting function is implicitly defined from a three-dimensional integral, which brings great difficulty both in analysis and in numerical simulation. On the other hand, if multiple moments are involved, using polynomial expansion leads to too many terms and loss of significant properties.

Quasi-entropy is an elementary function as a substitution, keeping the essential properties of the original entropy: strict convexity; positive definiteness of the covariance matrices; invariance under rotations; molecular symmetry consistent. We report a few simple applications in liquid crystals, including homogeneous phase transitions, closure approximations, and physical range preserving numerical schemes.