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 linear transport coefficients. The consequences of microreversibility and spatial symmetries are investigated, leading to the prediction of cross effects resulting from Onsager–Casimir reciprocal relations. Crystalline solids and liquid crystals are potential examples of application. The approach is clarifying the links between the microscopic Hamiltonian dynamics and the thermodynamic and transport properties at the macroscale.
Highlights
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
In nematic liquid crystals, the part of the Hamiltonian ruling the rotation of the system around the orientation selected by spontaneous symmetry breaking should be separated from the rest of the Hamiltonian function in order to define equilibrium probability distributions describing the properties of the phase with broken symmetry
We have shown that the macroscopic equations ruling the time evolution of matter with broken continuous symmetries can be derived in a unified microscopic approach based on the local equilibrium distribution, extending to crystalline solids and liquid crystals results previously obtained for normal fluids
Summary
The spontaneous breaking of continuous symmetries is a ubiquitous phenomenon in nature. Microscopic approach to the macrodynamics of matter with broken symmetries has been developed since the sixties [25,26,27,28,29,30,31,32,33,34,35], provides the microscopic expressions for the dissipativeless fluxes of Eulerian type, and local thermodynamics and the statistical-mechanical expression for entropy production in terms of the dissipative fluxes These latter fluxes can be obtained at leading order in the gradients of the macrofields together with the transport coefficients given by Green–Kubo formulas. Einstein’s convention of summation over repeated indices is adopted
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Statistical Mechanics: Theory and Experiment
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
