“The Garden of Earthly Delights,” Detail, Central Panel - Hieronymus Bosch

Last month, scientists met remotely to discuss two areas of study that are often at odds. The first, complex systems, typically deals with macroscopic scales, where systems evolve in constrained ways. Stochastic thermodynamics, on the other hand, has to date mostly focused on microscopic scales where systems such as proteins, molecules, or computational circuits can evolve with few constraints. 

The researchers are particularly interested in how to use tools from stochastic thermodynamics to analyze complex systems like the economy, or ecosystems. 

Thermodynamics has long been investigating the properties of the entropy (“disorder”) in large systems that are in thermal equilibrium, or a steady state. One famous result is the second law of thermodynamics, which says that the entropy of an isolated system cannot decrease. A classic example of the second law is an egg which falls off a counter and splats on the ground, increasing its entropy. Time never seems to flow backwards, so the broken egg never reassembles itself and hops back onto the counter, which would decrease its entropy. 

However, at small scales, on the level of small numbers of atoms, the laws of conventional, macroscopic thermodynamics can begin to break down, says David Wolpert, a professor at SFI and a co-organizer of the meeting. For example, the second law goes somewhat awry; it’s often impossible to tell whether a movie of a small number of atoms is running forward or backward. 

For years, stochastic thermodynamics experts have been looking at the transition between these two regimes, an intermediate scale where entropy only usually increases, and where events usually seem to move forward in time. They now have theorems to exactly quantify this transitional regime.

The three-day virtual workshop held between SFI and Complexity Science Hub Vienna aimed to bring these newly hatched tools of stochastic thermodynamics to bear on the wide variety of problems in complex systems. “We started exploring what might come out if you start joining techniques from these fields,” says Wolpert. “It actually also serves a larger purpose, by making these communities more aware of one another, interacting with one another.”

Talks came from researchers studying both stochastic thermodynamics and complex systems. “I have the feeling that stochastic thermodynamics is related to complex systems,” said SFI External Professor Stefan Thurner, a complex systems theorist and President of CSH Vienna. He proposed that stochastic thermodynamics could be used to calculate properties of “small” complex systems. Other researchers looked for similar connections. Sosuke Ito, a researcher at the University of Tokyo, drew parallels between entropy and Fisher information, a concept used to understand the speed of information transfer in a complex system. 

Holding the meeting virtually also allowed dozens more participants than would otherwise have attended, and the organizers plan to make it an annual virtual event. “What happens outside the conference room is better in real life,” says Jan Korbel, a researcher at the CSH Vienna and meeting co-organizer. “What happens inside the conference room is better in a virtual workshop.”