We end by noting that the terminology "local detailed balance" comes from statistical physics , where it has become the central concept to formulate thermodynamically consistent dynamics . Its chemical counterpart (see SI equation S.33) is fully equivalent to usual conditions imposed on the rate constants to ensure that microscopic reversibility holds (see for instance equation 5 in reference 16). We note that use of the term "local detailed balance" in this context is considered contentious by some. For a more detailed discussion see SI section III.