Variance sum rule for entropy production

Area of Science:

• Non-equilibrium physics
• Statistical mechanics
• Soft matter physics
• Biophysics

Background:

• Entropy production quantifies irreversibility and dissipation in physics, crucial for understanding energy transduction.
• Measuring entropy production at the nanoscale is a significant challenge in nonequilibrium systems.
• Existing methods often lack the precision or applicability for complex nanoscale phenomena.

Purpose of the Study:

• To introduce a novel Variance Sum Rule (VSR) for measuring the rate of entropy production (σ) in nonequilibrium steady states.
• To demonstrate the VSR's applicability to systems with directly measurable forces and complex biological systems.
• To provide a new tool for quantifying irreversibility and dissipation at the nanoscale.

Main Methods:

• Development of a Variance Sum Rule (VSR) relating displacement and force variances.
• Application of VSR to an active Brownian particle in an optical trap.
• Experimental validation using flickering measurements in human red blood cells.

Main Results:

• The VSR successfully measures entropy production rate (σ) in nonequilibrium steady states.
• Spatially heterogeneous entropy production with a finite correlation length was observed in red blood cells.
• Average entropy production values obtained via VSR agree with independent calorimetry measurements.

Conclusions:

• The Variance Sum Rule (VSR) offers a practical method for measuring nanoscale entropy production.
• VSR is applicable to diverse systems, including active matter and biological cells.
• This work enables the derivation of entropy production using force spectroscopy and time-resolved imaging.