Information-theoretic limits of control

@article{Touchette2000InformationtheoreticLO,
  title={Information-theoretic limits of control},
  author={Touchette and Lloyd},
  journal={Physical review letters},
  year={2000},
  volume={84 6},
  pages={
          1156-9
        }
}
  • Touchette, Lloyd
  • Published 26 May 1999
  • Computer Science, Physics, Medicine
  • Physical review letters
Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of control systems shows feedback control to be a zero sum game: each bit of information gathered from a dynamical system by a control device can serve to… 
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  • T. Sagawa, Masahito Ueda
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
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A general theory of feedback control on classical stochastic thermodynamic systems is established and nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality are generalized.
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The state-of-the-art and the main open problems that include aspects of the redundancy of correlated operations of feedback control and the continuous operation of feedback controlled systems are presented.
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The fluctuation theorem is established in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, and the resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange.
Towards quantum cybernetics
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Fundamental limits to the controllability of an open system can be formalized in terms of the law of requisite variety, which is derived from the second law of thermodynamics and suggests that establishing correlations between the system of interest and a controller is beneficial.
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A brief survey of control and synchronization under information constraints (limited information capacity of the coupling channel) is given and it is shown that the upper bound of the limit synchronization error (LSE) is proportional to the upper Bound of the transmission error.
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