One of the major resource requirements of computers — ranging from biological cells to human brains to digital computers — are the free energy costs in running them. These thermodynamic properties of computers have been a long-standing focus of research in statistical physics, going back (at least) to the early semi-formal work of Maxwell and of Szilard.

Recent revolutionary breakthroughs in stochastic thermodynamics are allowing us for the first time to analyze the thermodynamics of computers in a fully rigorous manner. Here I illustrate some of these recent results, including the thermodynamic costs of (loop-free) digital circuits, of Turing machines, and of asynchronous distributed computers like the interacting organelles in a cell.