Optimum capacity and full counting statistics of information content and heat quantity in the steady state

We consider a bipartite quantum conductor and analyze fluctuations of heat quantity in a subsystem as well as self-information associated with the reduced-density matrix of the subsystem. By exploiting the multicontour Keldysh technique, we calculate the Renyi entropy, or the information-generating function, subjected to the constraint of the local heat quantity of the subsystem, from which the probability distribution of conditional self-information is derived. We present an equality that relates the optimum capacity of information transmission and the Renyi entropy of order 0, which is the number of integer partitions into distinct parts. We apply our formalism to a two-terminal quantum dot. We point out that in the steady state, the reduced-density matrix and the operator of the local heat quantity of the subsystem may be commutative.