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We consider a bipartite quantum conductor and analyze fluctuations of heatquantity in a subsystem as well as self-information associated with thereduced-density matrix of the subsystem. By exploiting the multi-contourKeldysh technique, we calculate the R\'enyi entropy, or the informationgenerating function, subjected to the constraint of the local heat quantity ofthe subsystem, from which the probability distribution of conditionalself-information is derived. We present an equality that relates the optimumcapacity of information transmission and the R\'enyi entropy of order 0, whichis the number of integer partitions into distinct parts. We apply our formalismto a two-terminal quantum dot. We point out that in the steady state, thereduced-density matrix and the operator of the local heat quantity of thesubsystem may be commutative.

Full-counting statistics of information content and heat quantity in the steady state and the optimum capacity