Energy-Time-Accuracy Tradeoffs in Thermodynamic Computing

2026-01-07

AI Summary

This work addresses the lack of a universal theoretical framework characterizing the fundamental trade-offs among energy, time, and accuracy in thermodynamic computation. By integrating nonequilibrium Langevin dynamics, geometric bounds on entropy production, and stochastic control theory, the authors derive for the first time a universal lower bound on the energy–delay–dissipation product (EDDP). They further propose a near-optimal driving protocol that requires no prior knowledge of the target distribution. When applied to matrix inversion tasks in an overdamped quadratic system, the protocol approaches the theoretical limit even without knowing the final equilibrium state, demonstrating robust performance across diverse potential landscapes.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In the paradigm of thermodynamic computing, instead of behaving deterministically, hardware undergoes a stochastic process in order to sample from a distribution of interest. While it has been hypothesized that thermodynamic computers may achieve better energy efficiency and performance, a theoretical characterization of the resource cost of thermodynamic computations is still lacking. Here, we analyze the fundamental trade-offs between computational accuracy, energy dissipation, and time in thermodynamic computing. Using geometric bounds on entropy production, we derive general limits on the energy-delay-deficiency product (EDDP), a stochastic generalization of the traditional energy-delay product (EDP). While these limits can in principle be saturated, the corresponding optimal driving protocols require full knowledge of the final equilibrium distribution, i.e., the solution itself. To overcome this limitation, we develop quasi-optimal control schemes that require no prior information of the solution and demonstrate their performance for matrix inversion in overdamped quadratic systems. The derived bounds extend beyond this setting to more general potentials, being directly relevant to recent proposals based on non-equilibrium Langevin dynamics.

Problem

• thermodynamic computing
• energy-time-accuracy tradeoffs
• entropy production
• energy-delay-deficiency product
• stochastic computation

Innovation

• thermodynamic computing
• energy-delay-accuracy tradeoff
• entropy production bounds
• quasi-optimal control
• non-equilibrium Langevin dynamics