Fluctuation and Dissipation in Liquid-Crystal Electroconvection

Abstract

In this experiment a steady state current is maintained through a liquid crystal thin film. When the applied voltage is increased through a threshold, a phase transition is observed into a convective state characterized by the chaotic motion of rolls. Above the threshold, an increase in power consumption is observed that is manifested by an increase in the mean conductivity. A sharp increase in the ratio of the power fluctuations to the mean power dissipated is observed above the transition. This ratio is compared to the predictions of the fluctuation theorem of Gallavotti and Cohen using an effective temperature associated with the rolls' chaotic motion.PACS numbers: 05.70.Ln, 47.52.+j The fluctuation-dissipation theorem relates the spontaneous fluctuations in a system at temperature T with its response to an external driving force. An example might be a simple harmonic oscillator surrounded by air. The air molecules exponentially damp its periodic motion and also cause the oscillating mass to fluctuate about its equilibrium position [1].The experiment described here is concerned, not with a system in thermal equilibrium but rather, one which is in a steady state: an electric potential V applied across a weakly conducting liquid crystal (LC), generates convective motion within it when V exceeds a critical value V c [2]. The LC is in good contact with its surroundings, so that it's temperature is fixed at the ambient value T , as it dissipates power P at a mean rate P . Our interest centers on the dependence of P and its rms fluctuations σ P as a function of V or, equivalently, the control. Recently, Gallavotti and Cohen (GC) [4] have generalized the fluctuation-dissipation theorem (FDT) to include systems that are driven far from equilibrium, like the one studied here. While their work motivated the present experiment, we are unable to verify its central prediction concerning the probability density function π(P ). They showed that, under appropriate conditions, the system, assumed to be driven into a chaotic state, experiences such large fluctuations in P that sometimes P can become negative, i.e. the driven, dissipative system momentarily can send energy back into the power supply that generates the chaotic fluctuations. The theory makes a firm prediction about the ratio, π(P )/π(−P ).The GC theory is formulated in terms of the entropy production rate s τ =Ṡ τ , which is related to the average power gained by the system during a time period τ by s τ = P τ /kT ss . Here the steady state temperature kT ss is equal to the mean kinetic energy per particle. The authors show that if the chaotic motion in the system satisfies certain conditions, thenThe theorem, which GC call the fluctuation theorem (FT), has been generalized by Kurchan [5] to systems undergoing Langevin dynamics and by Lebowitz and Spohn to general Markov processes [6]. The FT reduces to the FDT in the limit of vanishing driving force [7].For a macroscopic system like ours, it was not possible to achieve such large fluctuations in P that rende...

Persistent global power fluctuations near a dynamic transition in electroconvection

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“…The details of the experimental setup for the electric power fluctuation measurements have been presented elsewhere [9,10,11]. The set-ups permit the recording of both P (t) and the optical patterns, while at the same time monitoring the transmitted light intensity I(t) integrated over the entire area of the sample.…”

Distribution of Injected Power Fluctuations in Electroconvection

“…The study of the average injected power and fluctuations in quantity in EHC has been established in Refs. [15][16][17]. This method opens new routes in investigations of EHC.…”

Asymmetric Response of a Jammed Plastic Bead Raft

“…In this case, the probability distribution of an appropriate macroscopic variable, such as the power or stress, is studied, and the temperature is related to various measures of this distribution. This approach has been used in turbulent fluid systems [4,5,6] and driven complex fluids [7,8].In this paper, we focus on definitions of effective temperature based on the relationship between linear response functions and correlation functions [9,10]. There are two basic approaches: static response theory relating equal time fluctuations with infinite-time response and time-dependent methods.…”

“…In this case, the probability distribution of an appropriate macroscopic variable, such as the power or stress, is studied, and the temperature is related to various measures of this distribution. This approach has been used in turbulent fluid systems [4,5,6] and driven complex fluids [7,8].…”