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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Constraints in nonequilibrium thermodynamics: General framework and application to multicomponent diffusion.

Hans Christian Ottinger¹

¹Department of Materials, Polymer Physics, ETH Zurich, HCI H 543, CH-8093 Zurich, Switzerland. hco@mat.ethz.ch

The Journal of Chemical Physics

|March 26, 2009

Summary

This summary is machine-generated.

This study integrates holonomic constraints into the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework. This approach resolves ambiguities in classical thermodynamics, offering a more rigorous description of complex systems.

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Area of Science:

Thermodynamics
Statistical Mechanics
Mathematical Physics

Background:

Classical thermodynamics of irreversible processes can present ambiguities when using redundant variables.
Existing frameworks may not readily accommodate holonomic constraints in nonequilibrium systems.

Purpose of the Study:

To extend the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework to incorporate holonomic constraints.
To develop a more rigorous and unambiguous thermodynamic description for constrained nonequilibrium systems.
To illustrate the practical application of this extended framework.

Main Methods:

Extension of Dirac's constrained Poisson bracket formalism to dissipative brackets.
Integration of holonomic constraints within the GENERIC framework.
Development of a symmetric thermodynamic description for diffusion in multicomponent systems.
Application of an incompressibility constraint as a specific example.

Main Results:

A method for incorporating holonomic constraints into the GENERIC framework has been successfully developed.
The extended GENERIC framework provides a more elaborate and restrictive structure compared to classical approaches.
Ambiguities present in classical thermodynamics of irreversible processes, particularly with redundant variables, are resolved.

Conclusions:

The incorporation of holonomic constraints into GENERIC offers a powerful and unambiguous approach to nonequilibrium thermodynamics.
This method facilitates a more precise description of physical systems, such as multicomponent diffusion and incompressible fluids.
The developed framework enhances the predictive and descriptive capabilities of thermodynamic modeling for complex systems.