Stochastische Thermodynamik in getriebenen Kolloidsystemen
Final Report Abstract
In this project we report on experiments on colloidal systems driven away from thermal equilibrium. In all experiments we use optical tweezers to create a controlled nonequilibrium situation. With video microscopy we detect the particle’s position and the full phase space trajectory is accessible. First we investigated the dynamical properties of nonequilibrium stationary states (NESS) and the relaxation behavior of such states. Our results show that the NESS relaxation time is independent of the initial conditions from which the relaxation process starts. In contrast to an overdamped equilibrium system, where the relaxation is purely exponential, now observables oscillate during the relaxation process. In addition, we show that the relaxation time is identical to that obtained from the decay of the velocity autocorrelation function in the steady-state regime, i.e. after relaxation has been completed. In agreement with theoretical calculations the relaxation time increases when driving the system further away from thermal equilibrium. Although the details of nonequilibrium relaxation processes are different and deviations from the equilibrium Ornstein Uhlenbeck result are prominent, the basic principles having a universal relaxation time determinable via stationary fluctuations are the same. The situation becomes different when focussing on the fluctuation dissipation-theorem (FDT). Only valid in thermal equilibrium its violation is a clear fingerprint of a nonequilibrium system and in our experiment response and correlations differ by more than a factor of 10. As recently theoretically predicted our results verify that, by using different conjugate variables, the validity of the FDT is extendable to stationary nonequilibrium states. We experimentally verified two independent generalizations of the FDT. Most remarkably is the fact that the equilibrium form of the FDT can be kept when the conjugate variable is not taken with respect to energy, but with respect to entropy. Although the different variants of the FDT are from a theoretical point of view equivalent, large differences regarding the size of experimental errors exist. Therefore, the right choice of observables is important for the accurate determination of the response via stationary measurements. To investigate more realistic nonequilibrium systems with interactions and many degrees of freedom, we studied a driven two particle system where the repulsive interaction between the particles is adjustable via magnetic dipolar forces. The stochatic motion, now an interplay between driven motion in a tilted potential, diffusion and interactions obeys an enhanced maximum in diffusion as a function of the interaction strength. Additionally we were investigating a miniaturized heat engine, brought down to length and energy scales where fluctuations matter. In our microscopic model system the working gas and the piston of its macroscopic counterpart are replaced by a colloidal particle which is confined to a laser trap with variable trap stiffness. When moving the system along a Stirling cycle the machine converts heat into work. The work, now a fluctuating quantity, strongly depends on the cycle duration time τ . With increasing τ , the efficiency of our heat engine increases until it reaches the corresponding theoretical value. These experiments provide fundamental insights into the conversion of thermal energy to mechanical work on a microscopic level. Using the experimental tools developed in this project the investigation of new nonequilibrium systems becomes accessible. (i) The the ability to control paramagnetic particles with laser tweezers opens the possibility to investigate nonequilibrium systems where the driving mechanism is not caused by time dependent or nonconservative external fields but created by a temporal variation of an internal degree of freedom, the tunable repulsive magnetic interaction between the colloidal particles. (ii) The ability to precisely control the bath temperature via an infrared laser allows to investigate systems which react sensitively on temperature changes. Examples here are e.g. PNIPAM, or DNA grafted particles [1, 2] which change their size or binding behavior when changing the environment temperature. Since most of the experiments on these systems were made under quasistatic temperature conditions, we would be able to study the systems reaction after very fast temperature changes.
Publications
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Stochastic thermodynamics of nonequilibrium stationary states Conference: Liquid matter, Lund, Sweden (2008)
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Relaxation of a colloidal particle into a nonequilibrium steady state, Phys. Rev. E, 79 060104(R), (2009)
V. Blickle, J. Mehl, C. Bechinger
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Colloidal particles as probes for stochastic thermodynamics Conference: Optimization in stochastic nano-systems, Delmenhorst, Germany (2010)
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Experimental accessibility of generalized fluctuation-dissipation relations for nonequilibrium steady states Phys. Rev. E, 82 032401, (2010)
J. Mehl, V. Blickle, U. Seifert , C. Bechinger
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Wetting of surfaces covered by elastic hairs, Langmuir, 26 (10) 7233, (2010)
N.R. Bernardino, V. Blickle, S. Dietrich
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Colloidal particles as probes for stochastic thermodynamics Conference: Thermodynamics - can macro learn from nano, Snogeholm, Sweden (2011)
