  All previously derived thermodynamic fluctuation theorems (FTs) that concern
multiple co-evolving systems have required that each system can only change its
state during an associated pre-fixed, limited set of time intervals. However,
in many real-world cases the times when systems change their states are
randomly determined, e.g., in almost all biological examples of co-evolving
systems. Such randomness in the timing drastically modifies the thermodynamics.
Here I derive FTs that apply whether or not the timing is random. These FTs
provide new versions of the second law, and of all conventional thermodynamic
uncertainty relations (TURs). These new results are often stronger than the
conventional versions, which ignore how an overall system may decompose into a
set of co-evolving systems. In addition, the new TURs often bound entropy
production (EP) of the overall system even if none of the criteria for a
conventional TUR (e.g., being a non-equilibrium steady state) hold for that
overall system.
