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Optimal control in nonequilibrium systems: Dynamic Riemannian geometry of the Ising model.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Optimal control in nonequilibrium systems is key to understanding nanoscale machines.
  • Existing frameworks use Riemannian geometry for analytically solvable systems.
  • Thermodynamic geometry is not well-described for systems lacking analytical solutions.

Purpose of the Study:

  • To numerically construct the dynamic metric for thermodynamic geometry.
  • To investigate optimal control protocols for magnetization reversal.
  • To explore the application of geometric principles to complex, non-analytically solvable systems.

Main Methods:

  • Numerical construction of the dynamic metric.
  • Application to the two-dimensional Ising model.
  • Analysis of control protocols for magnetization reversal.

Main Results:

  • Successfully constructed the dynamic metric for a complex system.
  • Identified specific optimal protocols for magnetization reversal.
  • Demonstrated the utility of thermodynamic geometry beyond analytically solvable models.

Conclusions:

  • Numerical methods can effectively describe thermodynamic geometry in complex systems.
  • Optimal control protocols minimize dissipation in magnetization reversal.
  • This approach offers insights into controlling nonequilibrium nanoscale systems.