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Heat flow due to time-delayed feedback.

Sarah A M Loos1, Sabine H L Klapp2

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Time delays in stochastic systems cause heat flow, even with minimal delay. This study explores the thermodynamics of delayed systems, revealing noise and delay interplay drives this effect, impacting systems from physics to technology.

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Area of Science:

  • Thermodynamics of stochastic systems
  • Non-Markovian processes
  • Nonlinear dynamics

Background:

  • Discrete time delays are common in stochastic systems across science and technology.
  • Delays can cause oscillations and resonance due to noise interaction.
  • Thermodynamics of delayed systems, especially nonlinear ones, remains underexplored.

Purpose of the Study:

  • To develop an analytical approach for heat rates in delayed feedback systems.
  • To investigate the thermodynamics of classical overdamped systems with time-delayed feedback.
  • To understand the role of noise and delay in heat flow.

Main Methods:

  • Analytical approach for net steady-state heat rate calculation.
  • Analysis of classical overdamped systems with time-delayed feedback.
  • Comparison with underdamped systems exhibiting "entropy pumping".

Main Results:

  • Time-delayed feedback inevitably induces a finite heat flow, even for vanishingly small delays.
  • The interplay between noise and delay is identified as the cause of heat flow.
  • In bistable systems, feedback can lead to heating or cooling and influences entropy production.

Conclusions:

  • Delayed feedback fundamentally alters the thermodynamics of stochastic systems.
  • The findings are measurable in experiments, such as with colloidal suspensions.
  • This work opens new avenues for exploring delayed stochastic thermodynamics.