Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Metastable Dynamical Computing with Energy Landscapes: A Primer

Christian Z. Pratt, Kyle J. Ray, James P. Crutchfield

TL;DR

CMOS-era computing imposes substantial energy costs, motivating alternative paradigms. This work advocates dynamical landscape computing, where information is encoded in metastable minima of a potential $U(x)$ coupled to a heat bath, and computation proceeds by reshaping the landscape while tracking fixed-point bifurcations. It analyzes 1-bit erasure via two bifurcation-based protocols—pitchfork (adiabatic, potentially reaching $k_B T \ln 2$ per bit) and saddle-node (irreversible and more dissipative)—and demonstrates a 2-bit control erasure in a quadruple-well landscape using a saddle-node mechanism. The framework integrates dynamical systems with nonequilibrium thermodynamics, offering a path to scalable, energy-efficient logic with higher-dimensional computations and optimized thermodynamic costs.

Abstract

Smartphones, laptops, and data centers are CMOS-based technologies that ushered our world into the information age of the 21st century. Despite their advantages for scalable computing, their implementations come with surprisingly large energetic costs. This challenge has revitalized scientific and engineering interest in energy-efficient information-processing designs. One current paradigm -- dynamical computing -- controls the location and shape of minima in potential energy landscapes that are connected to a thermal environment. The landscape supports distinguishable metastable energy minima that serve as a system's mesoscopic memory states. Information is represented by microstate distributions. Dynamically manipulating the memory states then corresponds to information processing. This framing provides a natural description of the associated thermodynamic transformations and required resources. Appealing to bifurcation theory, a computational protocol in the metastable regime can be analyzed by tracking the evolution of fixed points in the state space. We illustrate the paradigm's capabilities by performing 1-bit and 2-bit computations with double-well and quadruple-well potentials, respectively. These illustrate how dynamical computing can serve as a basis for designing universal logic gates and investigating their out-of-equilibrium thermodynamic performance.

Metastable Dynamical Computing with Energy Landscapes: A Primer

TL;DR

CMOS-era computing imposes substantial energy costs, motivating alternative paradigms. This work advocates dynamical landscape computing, where information is encoded in metastable minima of a potential coupled to a heat bath, and computation proceeds by reshaping the landscape while tracking fixed-point bifurcations. It analyzes 1-bit erasure via two bifurcation-based protocols—pitchfork (adiabatic, potentially reaching per bit) and saddle-node (irreversible and more dissipative)—and demonstrates a 2-bit control erasure in a quadruple-well landscape using a saddle-node mechanism. The framework integrates dynamical systems with nonequilibrium thermodynamics, offering a path to scalable, energy-efficient logic with higher-dimensional computations and optimized thermodynamic costs.

Abstract

Smartphones, laptops, and data centers are CMOS-based technologies that ushered our world into the information age of the 21st century. Despite their advantages for scalable computing, their implementations come with surprisingly large energetic costs. This challenge has revitalized scientific and engineering interest in energy-efficient information-processing designs. One current paradigm -- dynamical computing -- controls the location and shape of minima in potential energy landscapes that are connected to a thermal environment. The landscape supports distinguishable metastable energy minima that serve as a system's mesoscopic memory states. Information is represented by microstate distributions. Dynamically manipulating the memory states then corresponds to information processing. This framing provides a natural description of the associated thermodynamic transformations and required resources. Appealing to bifurcation theory, a computational protocol in the metastable regime can be analyzed by tracking the evolution of fixed points in the state space. We illustrate the paradigm's capabilities by performing 1-bit and 2-bit computations with double-well and quadruple-well potentials, respectively. These illustrate how dynamical computing can serve as a basis for designing universal logic gates and investigating their out-of-equilibrium thermodynamic performance.
Paper Structure (8 sections, 8 equations, 5 figures)

This paper contains 8 sections, 8 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Foundations of Dynamical Landscape Computing
  3. Single-bit Erasure
  4. Pitchfork protocol
  5. Saddle-node protocol
  6. 2-bit Dynamical Computations
  7. Conclusion
  8. Impossibility of a Pitchfork Bifurcation in a Specific Landscape

Figures (5)

  • Figure 1: Building a potential energy landscape $U(x)$ that stores and processes a single bit of information. (a) Flat landscape. (b) Landscape with an arbitrary number of energy minima. (c) Instantiating two minima in the landscape, but with no thermal environment connection. (d) Two wells but with damped and noise-perturbed particle motion. (e) Double-well potential with a sufficiently large barrier height for stable information storage.
  • Figure 2: A pitchfork information erasure protocol inspired by the Restore-to-One (RT1) protocol Landauer_1961 from different dynamical perspectives, taken at different points in time. (a) RT1 protocol showing both possible initial particle locations that end in the $1$ state. (b) RT1 protocol only illustrating the potential's fixed points. (c) A dynamical view of information erasure, demonstrating that erasure protocols are easily understood using bifurcation theory. The blue (yellow) lines represent the stable (unstable) fixed point trajectories throughout the protocol. In the dynamical-systems language overall the protocol is quite simple---a reverse pitch-fork bifurcation followed by a reverse saddle-node bifurcation.
  • Figure 3: A saddle-node bifurcation information erasure protocol inspired by Ref. Landauer_1961. Differing from the pitchfork protocol, it can not be carried out infinitely slowly to make it adiabatic and energy inefficient. Throughout the entire protocol, there are two saddle-node bifurcations. (a) The evolution of the potential during the protocol when keeping track of the microstate distributions. (b) The same protocol, but following the landscape's fixed points. (c) The saddle-node erasure protocol in terms of the landscape's fixed points only.
  • Figure 4: Potential energy landscape that supports carrying out $2$-bit computations: (a) Illustrating the two-dimensional landscape $U(x, y)$ via a three-dimensional landscape plot above its projected contour plot. (b) Contour plot of $U(x, y)$ showing example memory-state instantiations.
  • Figure 5: Dynamical view of the control erasure (CE) protocol: (a) The CE characterized by the annihilation of the red and green fixed points in the third quadrant, while maintaining all other fixed points. (b) A dynamical skeleton of the CE that only shows the landscape's fixed points and flow fields. Blue (red) corresponds to stable (unstable) fixed points, as well as a grey local maxima. The steps of the protocol are as follows: (i) Initialization. (ii) Drop barrier separating the green (red) stable (unstable) fixed points, while maintaining all other fixed points. (iii) Just after the red-green fixed point annihilation.