As I understood the article, in one part of the experiment they set up alternate regions of heat and cold within a sample of graphite using interference patterns from two laser sources. When they turned off the lasers, instead of the hot regions dispersing their energy until the troughs were the same temperature, the hot regions "overshot", becoming cooler than the (former) troughs, with wave-like behaviour.
This seems to me like energy is momentarily flowing from a cooler region (the former "peaks") to a hotter area (the former "troughs").
Would a Real Physicist be kind enough to explain to me why this doesn't violate the 2nd law? Probably the answer is "you misunderstood".