How stochastic thermodynamics changes in systems with multiple interacting components*

Stochastic thermodynamics has resulted in profound new insights into the thermodynamic irreversibility of non-equilibrium processes at the scale of biological cells. These range from information-theoretic extensions of the second law, to fluctuation theorems governing the relative probabilities of amounts of entropy production (EP) in any particular sample of a non-equilibrium process, to thermodynamic uncertainty relations relating the expected EP of a process to the precisions of currents with it, to speed limits relating expected EP of the process to how fast the state space probability distribution changes. Almost all of this research has focused on systems with no internal structure, in the sense that they are not explicitly decomposed into a set of distinct, interacting subsystems. However, such internal structures are a crucial feature of very many systems of interest - especially in biology. Typically in systems with such structure the rate matrix of each subsystem i only depends on a proper subset of the remaining subsystems. Such dependency can be represented with a directed graph, connecting the subsystems. In this talk I summarize the many ways that the form of that directed graph modifies the standard results of stochastic thermodynamics. In particular, I show how the form of that graph: 1) specifies a strengthened form of the second law; 2) specifies "vector-valued" extensions of the fluctuation theorems, concerning the joint probability of the entropy productions of the subsystems; 3) specifies extensions of the thermodynamic uncertainty relations to relate entropy productions and current precisions among the subsystems; 4) specifies extensions of the thermodynamic speed limits, to involve the speeds of changes of the probability distributions of all of the subsystems as well as expected EP.