Understanding the energy costs of computing

Researchers from the Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC (Mallorca, Spain), the University of Colorado, the Santa Fe Institute, and the The Abdus Salam International Centre for Theoretical Physics (ICTP), have made advancements that refine our fundamental understanding of the energy demands of modern computers. The study, published in Physical Review X, presents a new theoretical framework to quantify these thermodynamic costs, even at an elementary level.

The team, led by IFISC (UIB-CSIC) researcher Gonzalo Manzano, has developed a methodology to quantify the minimal energy dissipation of computers performing specific tasks, without needing extensive details about the physical makeup of the computers themselves. This innovative approach utilizes advanced techniques from stochastic thermodynamics to address challenges such as the impact of logical irreversibility, and computations with an uncertain runtime.

Key to this research, entitled «Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times», is the application of principles and techniques commonly used in mathematics of finance, such as martingale theory, to handle the stochastic nature of real-world computations. The findings include universal relations for the energy fluctuations and limits for the energy costs of any computational task, enhancing our understanding of the second law of thermodynamics in the context of information processing.

The study not only refines the existing laws of thermodynamics in relation to computational tasks but also introduces crucial elements for accounting for fluctuations in processes far from equilibrium. These insights can be key for designing energy-efficient computing systems, which is increasingly critical in addressing the environmental impact of technology.

The implications of this research extend beyond traditional computational sciences. It also has potential applications in biological physics, particularly in understanding how living systems process information. By establishing new universal thermodynamic relations applicable to computation statistics, this work sets the stage for future innovations in multiple disciplines.

Manzano, G., Kardeş, G., Roldán, É., & Wolpert, D. H. (2024). Thermodynamics of Computations with Absolute Irreversibility, Unidirectional Transitions, and Stochastic Computation Times. Physical Review. X, 14(2). https://doi.org/10.1103/physrevx.14.021026

Image: Sketch of a computational machine model starting in logical state q₀ and finishing the computation when state q₂ is reached. During the evolution, the processing of information and the stochastic jumps in the machine state lead to energy dissipation into the environment.