Variance sum rule for entropy production

Abstract

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

Editor’s summary

Entropy in a closed system is a measure of the disorder or randomness and represents the energy unavailable to do work. Di Terlizzi et al . propose a method for evaluating the steady-state entropy production in nonequilibrium stochastic systems (see the Perspective by Roldán). This method is achieved using a variance sum rule that connects changes in positions with the forces required to restore those positions. The approach was verified using high-resolution experimental data on optically trapped Brownian particles and red blood cells, including stretching of the cells and contour fluctuations, a measure of the cells’ metabolic activity. —Marc S. Lavine

The entropy production rate is determined from the variances of the position and forces applied to a system of particles.

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

Editor’s summary

Entropy in a closed system is a measure of the disorder or randomness and represents the energy unavailable to do work. Di Terlizzi et al . propose a method for evaluating the steady-state entropy production in nonequilibrium stochastic systems (see the Perspective by Roldán). This method is achieved using a variance sum rule that connects changes in positions with the forces required to restore those positions. The approach was verified using high-resolution experimental data on optically trapped Brownian particles and red blood cells, including stretching of the cells and contour fluctuations, a measure of the cells’ metabolic activity. —Marc S. Lavine

The entropy production rate is determined from the variances of the position and forces applied to a system of particles.

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

Editor’s summary

Entropy in a closed system is a measure of the disorder or randomness and represents the energy unavailable to do work. Di Terlizzi et al . propose a method for evaluating the steady-state entropy production in nonequilibrium stochastic systems (see the Perspective by Roldán). This method is achieved using a variance sum rule that connects changes in positions with the forces required to restore those positions. The approach was verified using high-resolution experimental data on optically trapped Brownian particles and red blood cells, including stretching of the cells and contour fluctuations, a measure of the cells’ metabolic activity. —Marc S. Lavine

The entropy production rate is determined from the variances of the position and forces applied to a system of particles.