Energetics of Information: From Timekeeping to Computing

In this project, we aim to investigate the energetics of information processing by combining tools from statistical mechanics with recent advances in quantum and stochastic thermodynamics [1,2]. Information is a physical resource, and its manipulation is constrained by thermodynamic laws—an insight that goes back to Maxwell’s demon and Landauer’s principle. Despite the rapid progress in stochastic and quantum thermodynamics, many fundamental questions remain open regarding the ultimate energetic requirements of information processing at microscopic and quantum scales. Here, we will address some of these challenges in two main directions.

First, we will exploit statistical mechanics techniques—such as random walks and
first-passage processes—to go beyond average energetic costs and analyze fluctuations, variances, ergodicity breaking and extreme events. We will investigate optimal control strategies in both stochastic and quantum thermodynamics, aiming to optimize dynamical processes with respect to higher-order quantities rather than just mean values (see preliminary results in [3]). We will apply these results to information erasure and, at a later stage, the characterization of the minimal energetic cost of timekeeping, using models of clocks built from quantum systems coupled to thermal environments [4].

Second, we will address computation from a thermodynamic perspective. We will study the energetic requirements of analog models of computation, particularly (quantum) reservoir computing [5]. We will investigate both fundamental bounds and tradeoffs between entropy production and accuracy, as well as practical principles for energy-efficient implementations.

[1] J. Goold et al, J. Phys. A: Math. Theor. 49, 143001 (2016).
[2] U. Seifert, Phys. A: St. Mech. 504, 176-191(2018).
[3] Miller, Perarnau-Llobet, SciPost Phys. 14, 072 (2023).
[4] A. N. Pearson et al, Physical Review X 11 (2), 021029.
[5] A. Sannia et al, Quantum 8, 1291 (2024).

Master in one of these areas:

• Nanoscience and Nanotechnology
• Quantum Science and Technology
• Theoretical Physics (statistical mechanics, many-body physics, stochastic
  processes).

The PhD workplan includes (i) the compilation of previous work, (ii) the development of models and theoretical tools and (iii) the computational work to implement the models and reach an understanding of their properties.

Besides the academic background required, general programming skills (e.g. Python, R, parallel programming, …) would also represent an added value.

Martí Perarnau-Llobet is a member of the Quantum Information Group (GIQ) of the Department of Physics. GIQ’s research interests range from theoretical aspects of wuantum information (quantum Shannon theory, quantum statistical inference, quantum metrology, entanglement theory) over implementations of quantum information protocols (e.g., quantum optics and ultra-cold gases) to applications of quantum information theory in condensed matter systems, nonequilibrium statistical mechanics and dissipative quantum dynamics.

Vicenç Méndez is professor of the Statistical Physics Group of the Department of Physics. He has his expertise on stochastic phenomena, random walks, long-distance dispersal, and search and exploration patterns. It is part of the SGR ‘Ecoevolutionary responses of animals to climate change’ focused on understanding the response of biological populations to climate and other external forcing from a statistical physics approach.