# Full-counting statistics of information content and heat quantity in the steady state and the optimum capacity. (arXiv:1807.04338v2 [cond-mat.mes-hall] UPDATED)

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 multi-contour

Keldysh technique, we calculate the R\'enyi 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 R\'enyi 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.