Title: A lower bound of the fluctuation response relation violation under feedback control Abstract: The ideas of Maxwell’s demon have been discussed by many researchers. The relation between the information entropy and the work extracted under feedback control is lively discussed in the context of Maxwell’s demon. Recently the second law was generalized under feedback control and this generalization was tested using a trapped Brownian particle. In addition, feedback control of the Brownian motion has many useful applications ranging from a thermal noise cancellation in atomic force microscopy, to a cooling for investigating quantum effects in a mechanical system. In this poster, we study fluctuations of a Brownian particle in Langevin system under feedback control. We find a fundamental bound in the fluctuation response relation violation and cooling in the presence of measurement errors which are not negligible in experimental settings. We also find that this cooling bound is determined by the balance between the information obtained by the measurement for feedback control and the information lost as a result of the relaxation.