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Related Experiment Video

Updated: Jan 17, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
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Noise equals control.

Eric De Giuli1

  • 1Toronto Metropolitan University, Department of Physics, 350 Victoria St. Toronto, Ontario, Canada M5B 2K3.

Physical Review. E
|September 16, 2025
PubMed
Summary

Noise acts as a control in stochastic systems, guiding the most probable trajectories. This study identifies a "response" field as the control variable in complex systems, revealing nature

Area of Science:

  • Physics
  • Chemistry
  • Systems Biology

Background:

  • Stochastic systems exhibit a control-theoretic interpretation where noise functions as the control mechanism.
  • In the weak-noise limit, the most probable trajectory between states minimizes an action functional, akin to optimal control.
  • The Doi-Peliti formalism describes general Markov jump processes, but the role of the response field was unclear.

Purpose of the Study:

  • To establish a precise mathematical mapping between noise and control in stochastic systems.
  • To resolve the interpretational problem of the response field in field-theoretic descriptions of stochastic systems.
  • To provide a physical interpretation for the response field as a control variable steering rare trajectories.

Main Methods:

  • Application of the Doi-Peliti formalism to general Markov jump processes.

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  • Identification of the 'response' (or 'momentum') field π as the control variable.
  • Illustration of the noise-control mapping on multistable chemical reaction networks, unstable fixed points, stochastic resonance, and Brownian ratchets.

    • Main Results:

    • The response field π is identified as the control variable that steers stochastic systems along rare trajectories.
    • This resolves the interpretational ambiguity of the response field in field-theoretic descriptions.
    • The mapping is demonstrated across various complex systems, including chemical reactions and physical phenomena.

    Conclusions:

    • Nature continuously samples control strategies, with noise acting as the control.
    • The noise-control mapping justifies agential descriptions of stochastic phenomena.
    • This framework builds intuition for non-equilibrium statistical mechanics, noise-enhanced biological mechanisms, and emergent agential behavior.