Nonequilibrium temperatures in steady-state systems with conserved energy

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Non-equilibrium systems

Background:

• Lattice models with conserved quantities are crucial for understanding energy transport.
• Defining temperature in non-equilibrium systems remains a challenge.
• Existing fluctuation-dissipation relations may not fully capture non-equilibrium thermodynamics.

Purpose of the Study:

• To define and investigate a statistical temperature for a class of non-equilibrium lattice models.
• To compare this statistical temperature with the temperature derived from the fluctuation-dissipation relation.
• To establish a physically relevant temperature measure for isolated non-equilibrium systems.

Main Methods:

• Exact solutions for a subclass of lattice models.
• Computation of response functions.
• Numerical renormalization group (NRG) procedures.
• Mean-field theory for quantitative predictions.

Main Results:

• A statistical temperature, T(th), was defined analogous to the equilibrium micro-canonical ensemble.
• The fluctuation-dissipation temperature, T(FD), was found to differ from T(th) when the relation is linear.
• T(th) was shown to be more physically relevant, equalizing in subsystems of large isolated systems.
• A universal parameter describing deviation from equilibrium was identified across models.

Conclusions:

• The statistical temperature T(th) provides a more physically meaningful measure in non-equilibrium steady states.
• The identified deviation parameter offers a way to characterize non-equilibrium behavior universally.
• Mean-field theory yields quantitative predictions for this deviation parameter.