Entropy flow through near-critical quantum junctions

TL;DR

This paper develops formulas for entropy flow in near-critical quantum junctions, linking entropic admittance to energy-momentum tensor structure, and applies it to quantum Ising circuits to quantify information capacity.

Contribution

It introduces a formalism for calculating entropy flow and entropic admittance in near-critical quantum circuits, with explicit calculations for quantum Ising junctions.

Findings

Derived elementary formulas for entropy flow through quantum junctions.

Expressed entropic admittance in terms of chiral entropy current commutators.

Calculated the entropic admittance for quantum Ising junctions and re-derived the information capacity.

Abstract

This is the continuation of cond-mat/0505084. Elementary formulas are derived for the flow of entropy through a circuit junction in a near-critical quantum circuit, based on the structure of the energy-momentum tensor at the junction. The entropic admittance of a near-critical junction in a bulk-critical circuit is expressed in terms of commutators of the chiral entropy currents. The entropic admittance at low frequency, divided by the frequency, gives the change of the junction entropy with temperature -- the entropic `capacitance'. As an example, and as a check on the formalism, the entropic admittance is calculated explicitly for junctions in bulk-critical quantum Ising circuits (free fermions, massless in the bulk), in terms of the reflection matrix of the junction. The half-bit of information capacity per end of critical Ising wire is re-derived by integrating the entropic `capacitance' with respect to temperature, from T=0 to T=infinity.