8th Liquid Matter Conference September 6-10, 2011 Wien, Austria ...

Wed 711:10-14:00P5.159Numerical study on the thermodynamic relationinvolving the mutual information of a system under thelinear feedback controlHiroyuki Suzuki 1 and Youhei Fujitani 21 KEIO UNIVERSITY, 253-2 Kamihiroya, Tsurugashima-shi 350-2203, Saitama,Japan2 KEIO UNIVERSITY, Kanagawa, JapanThe second law of the thermodynamics tells W ≥ ∆F , where W denotes a work done toa system and ∆F is the Helmholtz free energy difference. Due to the Mawell’s demon [1],this inequality appears to break down under feedback control. Recently, it was generalizedso that it involves the mutual information [2, 3]. In our previous study [4], we studied onedimensional-shift of a charged Brownian particle in a finite-time interval under the feedbackcontrol with the Kalman filter, and found that a generalized inequality holds. However, thedifference between its both hand-sides cannot be made small enough. It is of interest how wecan make the difference smaller. We consider shifting a neutral Brownian particle trapped by aharmonic potential. The feedback control is performed on a force exerted on the device makingthe potential so that the following evaluation functional is smaller. The evaluation functionalcontains the average of the work done to the particle by the force and two terms involvingcontrol parameters. One is a term proportional to the average of the squared force, while theother is a term proportional to the average of the squared difference between the final positionand the destination. Solving differential equations numerically, we calculate the work under theoptimal control by changing magnitude of observational noise. It is found that the differencebecomes larger as the magnitude of the observational noise is larger. This is because the informationobtained by the measurement cannot be utilized for the feedback control efficiently then.[1] J. C. Maxwell, ”Theory of Heart” (Appleton, London 1871).[2] T, Sagawa, M. Ueda, Phy. Rev. Lett 100, 080403 (2008).[3] T, Sagawa, M. Ueda, Phy. Rev. Lett 104, 090602 (2010).[4] H. Suzuki, Y. Fujitani, J. Phys. Soc. Jpn 78, 074007 (2009).159