Free-energy inference from partial work measurements in small systems

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Single-Molecule Biophysics

Background:

• Fluctuation relations (FRs) are fundamental theoretical results for systems not in equilibrium.
• Verifying FRs necessitates measuring the total work done on a system, which is often challenging.
• Partial work measurements are common in experiments, posing difficulties for FR verification.

Purpose of the Study:

• To investigate the applicability of fluctuation relations in dual-trap optical tweezers experiments.
• To determine the correct method for measuring work in single-molecule pulling experiments using optical tweezers.
• To explore methods for inferring full work distributions and extracting information from partial measurements.

Main Methods:

• Performed single-molecule pulling experiments using dual-trap optical tweezers.
• Measured forces exerted by both traps during the pulling process.
• Analyzed work definitions based on forces from the moved trap, the stationary trap, and differential forces.

Main Results:

• Work must be measured using the force from the actively moved trap to satisfy fluctuation relations.
• Measuring force from the stationary trap leads to an incorrect work definition and fails FR verification.
• A differential force measurement definition is proposed for symmetric setups, showing faster convergence for free-energy calculations.

Conclusions:

• Correct work measurement in dual-trap experiments is crucial for validating fluctuation relations and extracting thermodynamic information.
• Partial work measurements can be used to infer full work distributions and system properties like hydrodynamic drag via FRs.
• This work highlights a novel application of FRs for extracting information about irreversible processes in small systems.