Jarzynski equality on work and free energy: Crystal indentation as a case study

Area of Science:

• Statistical mechanics
• Thermodynamics
• Computational physics

Background:

• The Jarzynski equality (JE) offers a theoretical bridge between non-equilibrium processes and equilibrium thermodynamics.
• Its derivation for Hamiltonian systems suggests broad applicability for determining free-energy variations experimentally or computationally.
• However, the physical relevance and applicability conditions of the JE remain critical for its interpretation.

Purpose of the Study:

• To critically analyze the applicability conditions of the Jarzynski equality (JE).
• To investigate whether the 'work' in the JE's Hamiltonian derivation aligns with thermodynamic or mechanical work.
• To assess the JE's verifiability in simulations of nanoscale deformations.

Main Methods:

• Analytical derivation and examination of the 'work' definition within the Hamiltonian framework of the JE.
• Molecular dynamics simulations of nano-indentation on crystalline surfaces, inducing elastic and plastic deformations.
• Comparative analysis of simulation results against the theoretical predictions of the JE.

Main Results:

• The 'work' quantity in the Hamiltonian derivation of the JE is not universally thermodynamic or mechanical.
• The JE's applicability is restricted to specific circumstances, challenging its apparent generality.
• Jarzynski equality verification in simulations of nano-indentation was found to be impossible and process-dependent.

Conclusions:

• The physical relevance of mathematical relations like the JE hinges on their applicability conditions.
• The JE's formal derivation does not guarantee its physical validity or utility in all non-equilibrium scenarios.
• Careful assessment of definitions and simulation outcomes is crucial for interpreting results derived from non-equilibrium theories.