Near-critical quantum circuits are ideal physical systems for asymptotically
large-scale quantum computers, because their low energy collective excitations
evolve reversibly, effectively isolated from the environment. The design of
reversible computers is constrained by the laws governing entropy flow within
the computer. In near-critical quantum circuits, entropy flows as a locally
conserved quantum current, obeying circuit laws analogous to the electric
circuit laws. The quantum entropy current is just the energy current divided by
the temperature. A quantum circuit made from a near-critical system (of
conventional type) is described by a relativistic 1+1 dimensional relativistic
quantum field theory on the circuit. The universal properties of the
energy-momentum tensor constrain the entropy flow characteristics of the
circuit components: the entropic conductivity of the quantum wires and the
entropic admittance of the quantum circuit junctions. For example,
near-critical quantum wires are always resistanceless inductors for entropy. A
universal formula is derived for the entropic conductivity:
\sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the
temperature, S the equilibrium entropy density and v the velocity of `light'.
The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega).
The thermal Drude weight is, universally, v^{2}S. This gives a way to measure
the entropy density directly.Comment: 2005 paper published 2017 in Kadanoff memorial issue of J Stat Phys
with revisions for clarity following referee's suggestions, arguments and
results unchanged, cross-posting now to quant-ph, 27 page