[Paper Review] Shortcuts to Thermodynamic Computing: The Cost of Fast and Faithful Erasure

Alexander B. Boyd, Ayoti Patra+2 more|arXiv (Cornell University)|Dec 28, 2018

Advanced Thermodynamics and Statistical Mechanics31 references4 citations

TL;DR

This paper proposes counterdiabatic control protocols for fast, accurate, and faithful erasure of information in overdamped Langevin systems, enabling finite-time thermodynamic computing beyond Landauer's bound. It shows that the additional work required—irreversibly dissipated—scales with computation rate, system size, and information storage robustness, and that perfect erasure in finite time is achievable with finite work.

ABSTRACT

Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations -- that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allows for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as the square of the information-storing system's length scale. As a paradigmatic example, we design shortcuts to erase a bit of information metastably stored in a double-well potential. Though dissipated work generally increases with erasure fidelity, we show that it is possible perform perfect erasure in finite time with finite work. We also show that the robustness of information storage affects the energetic cost of erasure---specifically, the dissipated work scales as the information lifetime of the bistable system. Our analysis exposes a rich and nuanced relationship between work, speed, size of the information-bearing degrees of freedom, storage robustness, and the difference between initial and final informational statistics.

Motivation & Objective

• To design finite-time protocols for reliable information processing that surpass the quasistatic limit of Landauer's principle.
• To quantify the energetic cost of rapid, accurate erasure in overdamped systems, particularly the excess work beyond Landauer's bound.
• To investigate how system size, storage robustness (information lifetime), and erasure fidelity influence the dissipated work.
• To demonstrate that perfect erasure in finite time is possible with finite, non-zero work using counterdiabatic potentials.
• To establish a quantitative link between the dynamics of the bias trajectory and the resulting dissipation in information processing.

Proposed method

• Uses counterdiabatic control to engineer potentials that guide the system along desired paths in finite time, avoiding diabatic transitions.
• Applies the formalism of shortcuts to adiabaticity to overdamped Fokker-Planck dynamics, ensuring no population leakage during computation.
• Derives the counterdiabatic potential $ V^{CD}(x,t) $ as a function of the time-dependent bias $ b(t) $, using the probability density $ p(x) $ and the system's drift.
• Expresses the total counterdiabatic work as $ igracevert W^{CD} igracevert = f_1[p(ullet)] \times f_2[b(ullet)] $, separating dependence on system properties and protocol dynamics.
• Employs a sinusoidal bias trajectory $ b(t) = b_i \cos^2(t\pi/2\tau) + b_f \sin^2(t\pi/2\tau) $ to ensure zero initial and final time derivatives, enabling equilibrium at endpoints.
• Analyzes the dissipated work via the functional $ f_2[b(ullet)] = \int_0^\tau \frac{\dot{b}^2}{b - b^2} dt $, showing proportionality to the square of the computation rate and Hellinger distance between initial and final distributions.

Experimental results

Research questions

• RQ1 What is the energetic cost of performing fast, faithful information erasure in finite time, beyond Landauer’s bound?
• RQ2 How does the dissipated work scale with the rate of computation and the size of the information-storing system?
• RQ3 Can perfect erasure be achieved in finite time with finite work, and what protocols enable this?
• RQ4 How does the robustness of information storage—quantified by the information lifetime—affect the energetic cost of erasure?
• RQ5 What is the optimal protocol for minimizing dissipation in finite-time erasure, and does the chosen sinusoidal bias trajectory achieve it?

Key findings

• The counterdiabatic work required for finite-time erasure is proportional to the square of the computation rate and the system’s length scale.
• The dissipated work scales with the inverse of the erasure time $ \tau $, with a maximum proportional to $ \pi^2 / \tau $ for perfect bit flipping.
• Perfect erasure in finite time is achievable with finite, non-zero work, demonstrating that Landauer’s bound is not a strict upper limit on speed.
• The energetic cost of erasure is directly proportional to the information lifetime of the bistable system, linking storage robustness to processing cost.
• The functional $ f_2[b(ullet)] $, which governs the dissipation, is minimized by a path satisfying the Euler-Lagrange equation, but the chosen sinusoidal protocol does not satisfy this condition and is therefore suboptimal.
• The counterdiabatic work is expressed as a product of two independent factors: one depending on the equilibrium potential $ p(x) $, and the other on the time evolution of the bias $ b(t) $, enabling modular analysis of system and protocol contributions.