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.

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