Dynamics of a Liquid Crystal close to the Fr\'eedericksz transition

We report experimental and numerical evidences that the dynamics of the director of a liquid crystal driven by an electric field close to the critical point of the Fr\'eedericksz Transition(FT) is not described by a Landau-Ginzburg (LG) equation as it is usually done in literature. The reasons are related to the very crude approximations done to obtain this equation, to the finite value of the anchoring energy and to small asymmetries on boundary conditions. We also discuss the difference between the use of LG equation for the statics and the dynamics. These results are useful in all cases where FT is used as an example for other orientational transitions

Energy flow between two hydrodynamically coupled particles kept at different effective temperatures

We measure the energy exchanged between two hydrodynamically coupled micron-sized Brownian particles trapped in water by two optical tweezers. The system is driven out of equilibrium by random forcing the position of one of the two particles. The forced particle behaves as it has an "effective temperature" higher than that of the other bead. This driving modifies the equilibrium variances and cross-correlation functions of the bead positions: we measure an energy flow between the particles and an instantaneous cross-correlation, proportional to the effective temperature difference between the two particles. A model of the interaction which is based on classical hydrodynamic coupling tensors is proposed. The theoretical and experimental results are in excellent agreement

Comment on ''Measurement of Effective Temperatures in an Aging Colloidal Glass''

We measure the fluctuations of the position of a silica bead trapped by an optical tweezers during the aging of a Laponite suspension. We find that the effective temperature is equal to the bath temperature

Information and thermodynamics: Experimental verification of Landauer's erasure principle

We present an experiment in which a one-bit memory is constructed, using a system of a single colloidal particle trapped in a modulated double-well potential. We measure the amount of heat dissipated to erase a bit and we establish that in the limit of long erasure cycles the mean dissipated heat saturates at the Landauer bound, i.e. the minimal quantity of heat necessarily produced to delete a classical bit of information. This result demonstrates the intimate link between information theory and thermodynamics. To stress this connection we also show that a detailed Jarzynski equality is verified, retrieving the Landauer's bound independently of the work done on the system. The experimental details are presented and the experimental errors carefully discusse

On the transient Fluctuation Dissipation Theorem after a quench at a critical point

The Modified Fluctuation Dissipation Theorem (MFDT) proposed by G. Verley et al. {\it (EPL 93, 10002, (2011))} for non equilibrium transient states is experimentally studied. We apply MFDT to the transient relaxation dynamics of the director of a liquid crystal after a quench close to the critical point of the Fr\'eedericksz transition (Ftr), which has several properties of a second order phase transition driven by an electric field. Although the standard Fluctuation Dissipation Theorem (FDT) is not satisfied, because the system is strongly out of equilibrium, the MFDT is perfectly verified during the transient in a system which is only partially described by Landau-Ginzburg (LG) equation, to which our observation are compared. The results can be useful in the study of material aging

Energy transfer between colloids via critical interactions

We report the observation of a temperature-controlled synchronization of two Brownian-particles in a binary mixture close to the critical point of the demixing transition. The two beads are trapped by two optical tweezers whose distance is periodically modulated. We notice that the motion synchronization of the two beads appears when the critical temperature is approached. In contrast, when the fluid is far from its critical temperature, the displacements of the two beads are uncorrelated. Small changes in temperature can radically change the global dynamics of the system. We show that the synchronisation is induced by the critical Casimir forces. Finally, we present the measure of the energy transfers inside the system produced by the critical interaction.Comment: 8 pages, 7 figure

Phase transition oscillations induced by a strongly focused laser beam

We report here the observation of a surprising phenomenon consisting in a oscillating phase transition which appears in a binary mixture, PMMA/3-octanone, when this is enlightened by a strongly focused infrared laser beam. PMMA/3-octanone has a UCST (Upper Critical Solution Temperature) which presents a critical point at temperature Tc = 306.6 K and volume fraction $\phi$c = 12.8 % [Crauste et al., ArXiv 1310.6720, 2012]. This oscillatory phenomenon appears because of thermophoretic and electrostriction effects and non-linear diffusion. We analyze these oscillations and we propose a simple model which includes the minimal ingredients to produce the oscillatory behavior. Phase transitions in binary mixtures are still a widely studied subject, specifically near the critical point where several interesting and not completely understood phenomena may appear, among them we recall the critical Casimir forces [2],[3], confinement effects [4], [5] and out-of-equilibrium dynamics after a quench. The perturbation of the binary mixtures by mean of external fields is also an important and recent field of investigation [6]. For example, a laser can induce interesting phenomena in demixing binary mixtures because the radiation pressure can deform the interface between the two phases and it can be used to measure the interface tension [7]. Depending on the nature of the binary mixtures, laser illumination can also lead to a mixing or demixing transition. In ref.[8], focused infrared laser light heats the medium initially in the homogeneous phase and causes a separation in the LCST (Low Critical Solution Temperature) system. The radiation pressure gradients in a laser beam also contribute in the aggregation of polymers , thus producing a phase transition. The local heating may induce thermophoretic forces which attract towards the laser beam one of the binary-mixture components [9]. Other forces like electrostriction can also be involved [10]. In this letter, we report a new phenomenon, which consists in an oscillating phase transition induced by a constant illumination from an infrared laser beam in the heterogeneous region of an UCST (Upper Critical Solution Temperature) binary mixture. Oscillation phenomena in phase transition have already been reported in slow cooling UCST [11],[12] but as far as we know, never induced by a stationary laser illumination. After describing our experimental setup , we will present the results. Then we will use a very simplified model which contains the main necessary physical ingredients to induce this oscillation phenomenon

Fluctuations in an aging system: absence of effective temperature in the sol-gel transition of a quenched gelatin sample

We study the fluctuations of a Brownian micro particle trapped with optical tweezers in a gelatin solution undergoing a fast local temperature quench below the sol-gel transition. Contrary to what was previously reported, we observe no anomalous fluctuations in the particle's position that could be interpreted in terms of an effective temperature. A careful analysis with ensemble averages shows only equilibrium-like properties for the fluctuations, even though the system is clearly aging. We also provide a detailed discussion on possible artifacts that could have been interpreted as an effective temperature, such as the presence of a drift or a mixing in time and ensemble averages in data analysis. These considerations are of general interest when dealing with non-ergodic or non-stationary systems

Detailed Jarzynski Equality applied on a Logically Irreversible Procedure

International audienceA single bit memory system is made with a brownian particle held by an optical tweezer in a double-well potential and the work necessary to erase the memory is measured. We show that the minimum of this work is close to the Landauer's bound only for very slow erasure procedure. Instead a detailed Jarzynski equality allows us to retrieve the Landauer's bound independently on the speed of this erasure procedure. For the two separated subprocesses, i.e. the transition from state 1 to state 0 and the transition from state 0 to state 0, the Jarzynski equality does not hold but the generalized version links the work done on the system to the probability that it returns to its initial state under the time-reversed procedure

A general fluctuation-response relation for noise variations and its application to driven hydrodynamic experiments

The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent nontrivial diffusivity matrices, as we show with an application to an experiment of two trapped and hydrodynamically coupled colloids, one of which is subject to an external random forcing that mimics an effective temperature. The nonequilibrium susceptibility of the energy to a variation of this driving is an example of our formulation, which improves an earlier version, as it does not depend on the time-discretization of the stochastic dynamics. This scheme holds for generic systems with additive noise and can be easily implemented numerically, thanks to matrix operations