Course description

Stochastic thermodynamics provides a theoretical framework for describing non-equilibrium processes at the level of fluctuating trajectories, where distinct values of thermodynamic quantities such as work, heat, and entropy production can be assigned to individual realizations of stochastic dynamics. Over the past three decades, this field has produced fundamental results, including the fluctuation theorems, thermodynamic uncertainty relations, and thermodynamic speed limits. As a result it has become a central tool for analyzing systems ranging from molecular machines and active matter to biological networks and information-processing devices. At the same time, the rapid growth of modern computing has brought renewed attention to the energetic costs of information processing, from the microscopic limits of bit erasure to the large-scale energy demands of contemporary digital technologies and artificial intelligence.

A central insight emerging from recent research is that computation can itself be viewed as a physical process subject to the laws of thermodynamics. We are uncovering new, fundamental laws of physics that govern the thermodynamics of computers operating in finite time, subject to noise, and having the kinds of distributed architecture found in real-world computers. Specifically, we are learning how the thermodynamic cost of computation depends on the logical task being performed, and also on the structure of correlations in the input, the physical constraints on control in the system implementing the computation, and the distributed architecture of that system. These findings reveal deep connections between stochastic thermodynamics, information theory, and theoretical computer science, and open a new framework for analyzing computation in both conventional and unconventional systems.

This intensive one-week course will provide a comprehensive introduction to the stochastic thermodynamics of computation. The course will cover the foundations of stochastic thermodynamics and some relevant computer science theory, followed by a systematic treatment of the thermodynamic costs of information processing. Topics will include Landauer’s principle and its generalizations, mismatch costs, constrained optimal control, and the role of correlations and modularity in computation. We will also discuss emerging perspectives on what it means for a physical system to compute and examine applications to digital circuits, neural and biological systems, and self-assembling structures. Participants will engage with both theoretical concepts and practical applications, gaining practical tools to analyze the energetic efficiency and physical limits of information processing systems.

Reading List

Online lectures

• Joint ICTP-SISSA Colloquium by Prof. David Wolpert on “The Stochastic Thermodynamics of Computation”
• Stochastic thermodynamics of Boolean circuits, finite automata and Turing machines
• WOST tutorial videos

Relevant articles

• Ensemble and trajectory thermodynamics: A brief introduction
• Is stochastic thermodynamics the key to understanding the energy costs of computation? 
• Entropy production bounds for systems running computer programs
• Quo vadis, stochastic thermodynamics?

Textbooks

• Stochastic Thermodynamics: An Introduction by Luca Peliti and Simone Pigolotti
• Stochastic Thermodynamics by Udo Seifert 
• Introduction to the theory of computation by Michael Sipser

Participation in DIS master classes is by invitation only.