  Energy in a multipartite quantum system appears from an operational
perspective to be distributed to some extent non-locally because of
correlations extant among the system's components. This non-locality allows
users to transfer, in effect, locally accessible energy between sites of
different system components by LOCC (local operations and classical
communication). Quantum energy teleportation is a three-step LOCC protocol,
accomplished without an external energy carrier, for effectively transferring
energy between two physically separated, but correlated, sites. We apply this
LOCC teleportation protocol to a model Heisenberg spin particle pair initially
in a quantum thermal Gibbs state, making temperature an explicit parameter. We
find in this setting that energy teleportation is possible at any temperature,
even at temperatures above the threshold where the particles' entanglement
vanishes. This shows for Gibbs spin states that entanglement is not
fundamentally necessary for energy teleportation; correlation other than
entanglement can suffice. Dissonance---quantum correlation in separable
states---is in this regard shown to be a quantum resource for energy
teleportation, more dissonance being consistently associated with greater
energy yield. We compare energy teleportation from particle A to B in Gibbs
states with direct local energy extraction by a general quantum operation on B
and find a temperature threshold below which energy extraction by a local
operation is impossible. This threshold delineates essentially two regimes: a
high temperature regime where entanglement vanishes and the teleportation
generated by other quantum correlations yields only vanishingly little energy
relative to local extraction and a second low-temperature teleportation regime
where energy is available at B only by teleportation.

Quantum Physics;General Relativity and Quantum Cosmology;High Energy Physics - Theory