Consider a solid body at some constant temperature. Heat is transported by conduction and radiation. The radiative component transports heat by the d-d electronic transitions which emit photons and they are absorbed by molecules somewhere else in the body. I presume that the direction of emission is quantum mechanically indeterministic. It seems that entropy will only hold by a law of large numbers and thus entropy is regularly violated on small scales with the probability of a certain magnitude of entropy violation decreasing with the size of the system. In other words, while very improbable, it could occur that in our body of constant temperature, a large number of photons could be emitted on one side of the body which is absorbed by the other side of the body. This would mean that heat can be radiatively transported from regions of low temperature to regions of high temperature. Although improbable for large bodies, it would also seem that this would be a regular occurrence over small scales and timescales. Thoughts?