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Optimal control of overdamped systems.

Patrick R Zulkowski1, Michael R DeWeese2

  • 1Department of Physics, University of California, Berkeley, California 94720, USA; Department of Mathematics, Berkeley City College, Berkeley, California 94704, USA; and Redwood Center for Theoretical Neuroscience, University of California, Berkeley, California 94720, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
PubMed
Summary

Researchers derived a simple formula for the inverse diffusion tensor in nonequilibrium physics. This allows calculating minimal dissipation for nanoscale technologies and molecular motors, showing it

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Area of Science:

  • Nonequilibrium physics
  • Thermodynamics
  • Nanoscale technologies

Background:

  • Nonequilibrium systems are crucial for nanoscale tech and understanding molecular biology.
  • Parameter space in driven systems exhibits Riemannian geometry from inverse diffusion tensor.
  • Optimizing transitions in these systems is key for technological advancement.

Purpose of the Study:

  • Derive a compact expression for the inverse diffusion tensor using only equilibrium information.
  • Compute minimal dissipation for small-scale information processing and molecular motor models.

Main Methods:

  • Derived a general formula for the inverse diffusion tensor.
  • Applied the formula to two model systems: information erasure and a molecular motor.
  • Calculated minimal dissipation for optimal protocols of varying durations.

Main Results:

  • A simple, equilibrium-based formula for the inverse diffusion tensor was obtained.
  • Minimal dissipation for optimal protocols scales as 1/τ for both information erasure and molecular motor models.
  • The dissipation form for information erasure differed from previous findings.

Conclusions:

  • The derived formula simplifies calculations for nonequilibrium systems.
  • Results provide insights into optimizing nanoscale devices and biological motors.
  • Minimal dissipation scaling offers a universal characteristic of optimal protocols.