Estimate of the free energy difference in mechanical systems from work fluctuations:experiments and models

Abstract

The work fluctuations of an oscillator in contact with a heat reservoir and driven outof equilibrium by an external force are studied experimentally. The oscillatordynamics is modelled by a Langevin equation. We find both experimentally andtheoretically that, if the driving force does not change the equilibrium properties ofthe thermal fluctuations of this mechanical system, the free energy differenceΔF between two equilibrium states can be exactly computed using the Jarzynski equality (JE) andthe Crooks relation (CR) independently of the timescale and amplitude of the driving force.The applicability limits for the JE and CR at very large driving forces are discussed. Finally,when the work fluctuations are Gaussian, we propose an alternative method to computeΔF which can be safely applied, even in cases where the JE and CRmight not hold. The results of this paper are useful to computeΔF in complex systems such as the biological ones.