Fluctuation theorem with two independent field parameters: The one-dimensional compressible Ising model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Non-equilibrium Thermodynamics

Background:

• Investigating nonequilibrium work in physical systems is crucial for understanding thermodynamics.
• The one-dimensional compressible Ising model provides a tractable framework for studying such phenomena.

Purpose of the Study:

• To analyze the mechanical and magnetic work performed on a one-dimensional compressible Ising model out of equilibrium.
• To demonstrate the validity of the Jarzynski equality in this specific model system.

Main Methods:

• Utilizing the harmonic approximation to integrate mechanical degrees of freedom.
• Deriving an effective Hamiltonian dependent on magnetic field and applied force.
• Leveraging the exact solvability of the one-dimensional model to calculate free energy differences.

Main Results:

• The effective Hamiltonian was determined, incorporating both magnetic field and mechanical force.
• The Jarzynski equality was shown to be valid for nonequilibrium paths.
• The validity of the Jarzynski theorem was confirmed across all rates of variation for the magnetic field and mechanical force.

Conclusions:

• The Jarzynski equality is a robust principle applicable to the one-dimensional compressible Ising model under nonequilibrium conditions.
• This work provides theoretical validation for the Jarzynski theorem in a specific, exactly soluble physical system.