The validity of the fluctuation theorem for entropy production as deduced from the observation of trajectories implicitly requires that all slow degrees of freedom are accessible. We experimentally investigate the role of hidden slow degrees of freedom in a system of two magnetically coupled driven colloidal particles. The apparent entropy production based on the observation of just one particle obeys a fluctuation theorem-like symmetry with a slope of 1 in the short time limit. For longer times, we find a constant slope, but different from 1. We present theoretical arguments for a generic linear behavior both for small and large apparent entropy production but not necessarily throughout. By fine-tuning experimental parameters, such an intermediate nonlinear behavior can indeed be recovered in our system as well.

The large deviation function for entropy production is calculated by solving a time-independent eigenvalue problem for a particle driven along a periodic potential. In an intermediate force regime, the large deviation function shows pronounced deviations from a Gaussian behavior with a characteristic "kink" at zero entropy production. Such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range.

For configurational changes of soft matter systems affected or caused by external hydrodynamic flow, we identify applied work, exchanged heat, and entropy change on the level of a single trajectory. These expressions guarantee invariance of stochastic thermodynamics under a change of frame of reference. As criterion for equilibrium \textit{vs.} nonequilibrium, zero \textit{vs.} nonzero applied work replaces detailed balance \textit{vs.} nonvanishing currents, since both latter criteria are shown to depend on the frame of reference. Our results are illustrated quantitatively by calculating the large deviation function for the entropy production of a dumbbell in shear flow

According to Harada and Sasa [Phys. Rev. Lett. 95, 130602 (2005)], heat production generated in a nonequilibrium steady state can be inferred from measuring response and correlation functions. In many colloidal systems, however, it is a nontrivial task to determine response functions, whereas details about spatial steady state trajectories are easily accessible. Using a simple conditional averaging procedure, we show how this fact can be exploited to reliably evaluate average heat production. We test this method using Brownian dynamics simulations, and apply it to experimental data of an interacting driven colloidal system.

We study the fluctuation-dissipation theorem for a Brownian particle driven into a nonequilibrium steady state experimentally. We validate two different theoretical variants of a generalized fluctuation-dissipation theorem. Furthermore, we demonstrate that the choice of observables crucially affects the accuracy of determining the nonequilibrium response from steady state nonequilibrium fluctuations. According to Onsager, in thermal equilibrium the reaction of a system to a small external perturbation and the decay of an internal fluctuation created by thermal noise are indistinguishable. This property, characteristic for the linear response around equilibrium, is expressed by the fluctuation-which relates the time-dependent response R a,h ͑t͒ of an observable a͑t͒ to a perturbation h to the correlation function between a͑t͒ and the derivative of the energy rate Ė with respect to h ͓1͔. Here, k B T is the thermal energy.Since the FDT allows to determine response properties such as mobilities or susceptibilities from equilibrium measurements of diffusivities or power spectra and vice versa, it has found widespread application in different scientific fields such as statistical mechanics, biophysics, chemical or solid state physics ͓2͔. In its original derivation the FDT holds only close to thermal equilibrium. Therefore, violations of the FDT are a clear fingerprint of a nonequilibrium system. So far, recent theoretical ͓3-8͔ and experimental progress ͓9͔ demonstrated that the FDT can also be extended to a specific class of nonequilibrium systems, i.e., nonequilibrium steady states ͑NESSs͒. In ͓8͔ it has been shown that a similar expression as in Eq. ͑1͒ can be obtained when the energy is replaced by the entropy within the correlation function on the right hand side. Furthermore, it was demonstrated that additional equivalent forms of the FDT exist, which in principle allows for infinitely many variants.In this Brief Report, we experimentally demonstrate the validity of the FDT in a NESS for two different variants. Although both are equivalent from a theoretical point of view, large differences regarding the size of experimental errors exist. Therefore, the right choice of observables is important for the accurate determination of the response in such measurements.Our experimental setup has been described in detail elsewhere ͓10-12͔ and will be discussed here only briefly. A colloidal silica particle of radius r = 0.65 m, immersed in water, is trapped within a three-dimensional torus of radius R = 1.18 m by means of scanning laser tweezers. Using video microscopy, we track the angular coordinate x of the particle with − R Յ x Ͻ R with a spatial and temporal accuracy of 10 nm and 15 ms, respectively. Since the torus is far away from the lower surface of the cuvette cell ͑approxi-mately 50 m͒, hydrodynamic interactions with the sample cell are negligible ͓13͔. The tweezers scanning motion exerts a nonconservative force f to the particle so that it circulates around the torus onto which an additional static sinusoida...