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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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Non-Markovian Feedback Control and Acausality: An Experimental Study.

Maxime Debiossac1, Martin Luc Rosinberg2, Eric Lutz3

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We experimentally investigated causality in thermodynamics using a nanoparticle with time-delayed feedback control. The study reveals that acausal feedback in time-reversed dynamics leaves a signature in fluctuation relations, even when not physically realizable.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • Causality is a fundamental assumption in non-equilibrium thermodynamics, particularly for fluctuation relations.
  • Time-delayed feedback control introduces non-Markovian dynamics, challenging standard assumptions.

Purpose of the Study:

  • To experimentally investigate the statistical properties of work and entropy production under time-delayed feedback control.
  • To explore the impact of acausal feedback on fluctuation relations in non-equilibrium systems.

Main Methods:

  • Utilizing an optically trapped, underdamped nanoparticle subjected to continuous time-delayed feedback.
  • Analyzing the non-equilibrium statistical properties of work and entropy production in the steady-state regime.

Main Results:

  • Demonstrated that acausal feedback, where time-reversed paths depend on future positions, is experimentally realized.
  • Observed a clear signature of acausality in fluctuation relations in the long-time limit.

Conclusions:

  • Acausality in feedback control can be experimentally observed and affects thermodynamic relations.
  • The findings challenge the traditional understanding of causality in non-equilibrium statistical mechanics.