Thermodynamic inference based on coarse-grained data or noisy measurements.

Area of Science:

• Single-molecule biophysics
• Statistical mechanics
• Thermodynamics

Background:

• Fluctuation theorems are crucial for free-energy calculations in nonequilibrium experiments.
• Noise and coarse-graining complicate accurate free-energy determination.

Purpose of the Study:

• To develop improved estimators for free-energy differences using fluctuation theorems.
• To address challenges in thermodynamic inference caused by measurement noise and coarse-graining.

Main Methods:

• Proposing and testing novel free-energy estimators based on fluctuation theorems.
• Analyzing the impact of noise, including effective temperature concepts.
• Investigating non-Gaussian work distributions and correlated errors.
• Examining delayed measurements using linear Langevin equations.

Main Results:

• Developed improved estimators for free-energy differences under various noise conditions.
• Characterized noise effects using an effective temperature dependent on signal-to-noise ratio for Gaussian work.
• Demonstrated the utility of improved estimators for non-Gaussian work and correlated errors.
• Showcased applicability to systems with measurement delays.

Conclusions:

• The proposed estimators enhance the accuracy of free-energy calculations from noisy biophysical experiments.
• Effective temperature is a useful concept for Gaussian work but improved estimators are needed otherwise.
• The methods are robust for complex scenarios including correlated errors and delays.