Symmetries and nonequilibrium thermodynamics.

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Group Theory

Background:

• Thermodynamic systems comprise numerous interacting identical subsystems.
• Understanding relaxation dynamics is crucial for predicting system behavior.

Purpose of the Study:

• To establish a direct relationship between thermodynamic relaxation dynamics and the symmetry group of subsystem Hamiltonians.
• To demonstrate how symmetry constraints influence the evolution of thermodynamic systems towards equilibrium.

Main Methods:

• Analyzing the connection between state transitions and the root system of the Hamiltonian's symmetry group.
• Formulating the system's evolution as linear differential equations based on thermodynamic forces.
• Describing the system's trajectory as the negative gradient of a potential function dependent on symmetry.

Main Results:

• Identified a close relationship between relaxation dynamics and symmetry groups.
• Showed that state transitions correspond to elements of the root system associated with the symmetry group.
• Demonstrated that system evolution can be modeled by linear differential equations in thermodynamic forces.

Conclusions:

• The symmetry group of the Hamiltonian fundamentally constrains the relaxation dynamics of thermodynamic systems.
• The trajectory in thermodynamic force space is governed by a potential function derived from symmetry properties.
• This framework offers new insights into the equilibrium dynamics of complex thermodynamic systems.