Stochastic thermodynamics, meet information theory

Ten years ago, SFI Professor David Wolpert set out to build a bridge between two scientific fields that might seem to have nothing to say to each other — computer-science theory and a branch of physics called stochastic thermodynamics. Computer-science theorists typically study the “resource cost” of computation — the number of iterations a computer requires to complete a calculation, for example, or the amount of memory needed. But, Wolpert says, there’s also an important energetic cost in computing — how much energy is required — that has not been thoroughly investigated. Physicists who study stochastic thermodynamics, on the other hand, study systems far out of thermal equilibrium, which means they require or
produce heat.

Wolpert recognized that computers operate far from thermal equilibrium: They require energy to run, and they produce heat as they do so. The mathematical tools of stochastic thermodynamics seemed like a perfect and obvious way to probe the energy dynamics of computations. “It was such a match made in heaven,” he says. He assumed that this intersection had already been thoroughly explored, but he was wrong. So, he set out to establish the fundamentals on his own and convince others to join him. “I knew it would probably take about a decade before the engine would really start turning over.” 

A decade has passed, and he says the engine is humming. From June 16 to June 20 at SFI’s Cowan campus, Wolpert and his SFI co-organizers hosted a working group — a follow-up to one held last year — that brought together researchers to explore ideas and forge collaborations between the two fields. Participants included computer scientists and physicists, representing three continents, who shared progress on existing projects, ideas for new ones, and brainstormed ways to forge the new mathematics required to explore fundamental ideas around the thermodynamics of computers. They’re lured into the field, says Wolpert, by the possibility of developing new mathematics. 

“We have no idea what’s coming next,” he says. The nascent collaborations could spin off in many possible directions. Almost every issue of concern in computer-science theory can be translated into terms of energetic costs rather than other kinds of resource costs. Then, these issues can be dissected, analyzed, and modeled by developing new mathematical tools, using thermodynamics. Boolean circuits, for example, are mathematical models of computation that carry out logical operations — and operate far from thermal equilibrium. Researchers at the meeting discussed using stochastic thermodynamics to better understand the energy cost of big communication networks and chemical computers, which use chemical reactions to compute instead of the usual components.

“Basically, every chapter in computer-science-theory textbooks” is fair game, says Wolpert. “It’s all happening.” The meeting participants are already planning the next meeting and exploring possible publications and future books on the emerging subfield, as well. 

“This is what SFI is all about,” he says. “Taking fields that never even knew one another existed and just getting them to finally bump into one another near the punch bowl. That was this meeting.”

Read more about the working group Stochastic Thermodynamics and Computer Science Theory II