# Failure of the work-Hamiltonian connection for free energy calculations

## TL;DR

This paper demonstrates that the commonly used work-Hamiltonian connection in statistical mechanics cannot be relied upon to accurately estimate free energy changes from single-molecule experiments or simulations, challenging a fundamental assumption.

## Contribution

The paper reveals a fundamental failure of the work-Hamiltonian connection in free energy calculations, highlighting limitations in current methods and suggesting the need for alternative approaches.

## Key findings

- The work-Hamiltonian connection does not reliably estimate free energy changes.
- Implications for single-molecule experiments and molecular simulations are significant.
- Potential avenues to overcome these limitations are discussed.

## Abstract

Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=\partial H(x,t)/ \partial t which connects the microscopic work W performed by a time-dependent force on the coordinate x with the corresponding Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as it is, cannot be used to estimate free energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.

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Source: https://tomesphere.com/paper/0704.0761