# Improving free-energy estimates from unidirectional work measurements: theory and experiment.

@article{Palassini2011ImprovingFE, title={Improving free-energy estimates from unidirectional work measurements: theory and experiment.}, author={Matteo Palassini and Felix Ritort}, journal={Physical review letters}, year={2011}, volume={107 6}, pages={ 060601 } }

We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the random energy model in a suitable scaling limit parametrized by (logN)/μ, where μ measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (logN)/μ. We show that these expressions…

## 56 Citations

Free energy measurements by the generalized fluctuation theorems: Theory and numerical study of a model filament.

- Medicine, PhysicsThe European physical journal. E, Soft matter
- 2020

The measured work - free energy relation is consistent with the results obtained from the generalized fluctuation theorems, and operational methods to improve the estimates at high pulling speed are discussed.

Free-energy inference from partial work measurements in small systems

- Physics, MedicineProceedings of the National Academy of Sciences
- 2014

It is shown how FRs can be used to infer the full work distribution from partial work measurements, and suggested that this kind of inference could represent a previously unidentified and general application of FRs to extract information about irreversible processes in small systems.

Convergence of single-step free energy perturbation

- Mathematics
- 2017

ABSTRACT The convergence of free energy perturbation (Zwanzig's equation) and its non-equilibrium extension (Jarzynski's equation) is herein investigated from a practical point of view. We focus on…

From free energy measurements to thermodynamic inference in nonequilibrium small systems

- Physics
- 2015

Fluctuation theorems (FTs), such as the Crooks or Jarzynski equalities (JEs), have become an important tool in single-molecule biophysics where they allow experimentalists to exploit thermal…

On the accurate estimation of free energies using the jarzynski equality

- Computer Science, MathematicsJ. Comput. Chem.
- 2019

It is shown that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality, and that, for Gaussian unidirectional work distributions, ΔF^FD is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family.

Equilibrium free energies from non-equilibrium trajectories with relaxation fluctuation spectroscopy

- Physics
- 2018

Recent advances in non-equilibrium statistical mechanics and single-molecule measurements have enabled the determination of equilibrium free energies from non-equilibrium work measurements for…

From free energy measurements to thermodynamic inference in nonequilibrium small systems

- 2015

Fluctuation theorems (FTs), such as theCrooks or Jarzynski equalities (JEs), have become an important tool in single-molecule biophysics where they allow experimentalists to exploit thermal…

On the Improvement of Free-Energy Calculation from Steered Molecular Dynamics Simulations Using Adaptive Stochastic Perturbation Protocols

- Physics, MedicinePloS one
- 2014

The protocols introduced are able to produce an acceptable estimate of PMF with a significantly reduced bias, even with very fast perturbation regimes, and can be adopted as practical and efficient tools for the analysis of mechanical properties of biological molecules.

Quantum work fluctuations in connection with the Jarzynski equality.

- Mathematics, PhysicsPhysical review. E
- 2017

It is discovered in this work that var(e^{-βW}) in both harmonic and anharmonic Hamiltonian systems can systematically diverge in nonadiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence.

Phase transition in the Jarzynski estimator of free energy differences.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This correspondence is further demonstrated in two examples of physical interest: the sudden compression of an ideal gas and adiabatic quasistatic volume changes in a dilute real gas.

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