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

TL;DR

This paper develops a quantum statistical framework to analyze fluctuations of heat and information in bipartite quantum conductors, deriving probability distributions and relations for optimal information capacity using advanced Keldysh techniques.

Contribution

It introduces a novel method to compute the joint fluctuations of heat and information in quantum systems and relates the optimal capacity to the Re9nyi entropy, applying it to quantum dots.

Findings

Derived the probability distribution of self-information conditioned on heat fluctuations.

Established an equality linking optimal information capacity to Re9nyi entropy of order 0.

Applied the formalism to a two-terminal quantum dot system.

Abstract

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.