Symmetry and Thermodynamic Bounds on Cross-Coupling Transport in Chiral Liquid Crystals

TL;DR

This paper extends the Leslie model for chiral liquid crystals by incorporating thermodynamic bounds and the Q-tensor, revealing how cross-coupling coefficients depend on order parameters and are constrained by thermodynamics.

Contribution

It introduces a thermodynamic framework to bound Leslie cross-coupling coefficients and links chirality effects to thermodynamic principles in liquid crystals.

Findings

Cross-coupling coefficients depend on the scalar order parameter.

Coefficients vanish in the isotropic phase.

Chirality induces torque from transport currents.

Abstract

We reformulate the Leslie effects that describe the dynamic cross-couplings in chiral liquid crystals driven by the transport of heat, electric charge, and mass. The Ericksen--Leslie model is extended in the linear response framework by representing nematic order with the Q-tensor. Subsequently, the thermodynamic uncertainty relation is applied to identify the upper bounds of the Leslie cross-coupling coefficients. We reveal that the cross-coupling coefficients are dependent on the scalar order parameter and vanish in the isotropic phase. In addition, the chirality of the phase allows torque induced by a transport current parallel to the director. The mutual signs of the Leslie thermohydrodynamic and thermomechanical coefficients are likely to be opposite in calamitic liquid crystals, as suggested by recent experimental observations. Our model is applicable to the thermal, chemical, and electrical Leslie effects. The present arguments suggest that a common underlying principle may govern both the Leslie effects and the thermal Edelstein effect in chiral solid crystals attributed to chiral phonons.