Reply to Comment on "Failure of the work-Hamiltonian connection for free-energy calculations" by Horowitz and Jarzynski

TL;DR

This paper critiques a previous comment by Horowitz and Jarzynski, clarifying the proper definition of work in free-energy calculations and highlighting the discrepancy in their harmonic system analysis.

Contribution

It clarifies the correct identification of work in free-energy calculations and explains why previous results do not align with classical physics in the macroscopic limit.

Findings

Incorrect work definition leads to non-classical free energy results

Proper force-displacement work recovers textbook energy change

Highlights importance of correct work identification in thermodynamics

Abstract

We show that the Comment [arXiv:0808.1224] by Horowitz and Jarzynski obtains as a main result a general free energy change for a harmonic system that in the macroscopic limit does not recover the textbook expression for the energy change of a Hookean spring. The reason is that Horowitz and Jarzynski improperly identify work with parametric changes of the Hamiltonian instead of with the standard quantity, force times displacement.