Quasi-entropy

Organizer

Chunmei Su 苏春梅 （YMSC）

Speaker

Jie Xu 徐劼 (CAS)

Time

Tues., 10:00-11:00 am, April 1, 2025

Venue

B627, Shuangqing Complex Building A

Abstract

Liquid crystals are featured by local anisotropy usually described by angular moment tensors. The free energy of tensors needs a stabilizing entropy term. When non-axisymmetric molecules are involved, two classical approaches to write down an entropy term, quartic polynomial and maximum entropy state, both become too complicated. Meanwhile, the maximum entropy state, particularly in cases of non-axisymmetric molecules, seems the only reasonable way of closure approximation in dynamics, but it would make the model not computable.

We propose an elementary-function substitution of the original entropy (by maximum entropy state), called quasi-entropy, aiming to resolve the above problems. The quasi-entropy maintains the essential properties of the original entropy: strict convexity; positive-definiteness of covariance matrix; rotational invariance; consistency in symmetry reduction. Homogeneous phase diagrams of several representative cases match well with classical results. A further application is deriving biaxial frame hydrodynamics from tensor model. Numerical schemes keeping physical constraints can also be constructed naturally using the properties of the quasi-entropy.