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

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.