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

Mathematical relations concerning particle systems require knowledge of the applicability conditions to become physically relevant and not merely formal. We illustrate this fact through the analysis of the Jarzynski equality (JE), whose derivation for Hamiltonian systems suggests that the equilibrium free-energy variations can be computational or experimentally determined in almost any kind of non-equilibrium processes. This apparent generality is surprising in a mechanical theory. Analytically, we show that the quantity called "work"in the Hamiltonian derivation of the JE is neither a thermodynamic quantity nor mechanical work, except in special circumstances to be singularly assessed. Through molecular dynamics simulations of elastic and plastic deformations induced via nano-indentation of crystalline surfaces that fall within the formal framework of the JE, we illustrate that the JE cannot be verified and that the results of this verification are process dependent.