Can we 'feel' the temperature of knowledge? Modelling scientific popularity dynamics via thermodynamics

Just like everything in nature, scientific topics flourish and perish. While existing literature well captures article's life-cycle via citation patterns, little is known about how scientific popularity and impact evolves for a specific topic. It would be most intuitive if we could 'feel' topic's activity just as we perceive the weather by temperature. Here, we conceive knowledge temperature to quantify topic overall popularity and impact through citation network dynamics. Knowledge temperature includes 2 parts. One part depicts lasting impact by assessing knowledge accumulation with an analogy between topic evolution and isobaric expansion. The other part gauges temporal changes in knowledge structure, an embodiment of short-term popularity, through the rate of entropy change with internal energy, 2 thermodynamic variables approximated via node degree and edge number. Our analysis of representative topics with size ranging from 1000 to over 30000 articles reveals that the key to flourishing is topics' ability in accumulating useful information for future knowledge generation. Topics particularly experience temperature surges when their knowledge structure is altered by influential articles. The spike is especially obvious when there appears a single non-trivial novel research focus or merging in topic structure. Overall, knowledge temperature manifests topics' distinct evolutionary cycles.