A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems

Abstract

Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, like nanomagnetic bits, finding optimal protocols is challenging, requiring detailed information about the dynamical fluctuations of the controlled system. We provide a new, physically transparent derivation of a metric tensor for which the length of a protocol is proportional to its dissipation. This perspective simplifies nonequilibrium optimization problems by recasting them in a geometric language. We then describe a numerical method, an instance of geometric minimum action methods, that enables computation of geodesics even when the number of control parameters is large. We apply these methods to two models of nanomagnetic bits: a simple Landau-Lifshitz-Gilbert description of a single magnetic spin controlled by two orthogonal magnetic fields and a two dimensional Ising model in which the field is spatially controlled. These calculations reveal nontrivial protocols for bit erasure and reversal, providing important, experimentally testable predictions for ultra-low power computing.

arXiv comment9 pages, 2 figures

References in corpus (21)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Brownian Carnot engine
• Measuring thermodynamic length
• Optimal finite-time processes in stochastic thermodynamics
• Thermodynamic metrics and optimal paths
• Switching of Perpendicularly Polarized Nanomagnets with Spin Orbit Torque without an External Magnetic Field by Engineering a Tilted Anisotropy
• Universal trade-off relation between power and efficiency for heat engines
• The geometry of thermodynamic control
• Variational and optimal control representations of conditioned and driven processes
• Adaptive importance sampling for control and inference
• Dynamic Riemannian Geometry of the Ising Model
• Analysis of slow transitions between nonequilibrium steady states
• Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise
• Optimal Control of Overdamped Systems
• Path Integral Control and State Dependent Feedback
• Near-optimal protocols in complex nonequilibrium transformations
• Automotion of Domain Walls for Spintronic Interconnects
• All Spin Nano-magnetic State Elements

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