Microscopic approach to the macrodynamics of matter with broken symmetries

TL;DR

This paper develops a unified hydrodynamic framework for condensed matter systems with broken symmetries, deriving transport properties and effects from microscopic principles, applicable to solids and liquid crystals.

Contribution

It introduces a generalized statistical-mechanical approach to derive hydrodynamic equations for systems with broken symmetries, including Green-Kubo formulas and symmetry-based predictions.

Findings

Derived hydrodynamic equations for broken symmetry phases.

Obtained Green-Kubo formulas for transport coefficients.

Predicted cross effects from Onsager-Casimir relations.

Abstract

A unified set of hydrodynamic equations describing condensed phases of matter with broken continuous symmetries is derived using a generalization of the statistical-mechanical approach based on the local equilibrium distribution. The dissipativeless and dissipative parts of the current densities and the entropy production are systematically deduced in this approach by expanding in powers of the gradients of the macrofields. Green-Kubo formulas are obtained for all the transport coefficients. The results apply to both crystalline solids and liquid crystals. The consequences of microreversibility and spatial symmetries are investigated, leading to the prediction of cross effects resulting from Onsager-Casimir reciprocal relations.