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.

The rapid development of modern science nowadays makes it rather challenging to pick out valuable ideas from massive scientific literature. Existing widely-adopted citation-based metrics are not adequate for measuring how well the idea presented by a single publication is developed and whether it is worth following. Here, inspired by traditional X-ray imaging, which returns internal structure imaging of real objects along with corresponding structure analysis, we propose Scientific X-ray, a framework that quantifies the development degree and development potential for any scientific idea through an assembly of ‘X-ray’ scanning, visualization and parsing operated on the citation network associated with a target publication. We pick all 71,431 scientific articles of citation counts over 1,000 as high-impact target publications among totally 204,664,199 publications that cover 16 disciplines spanning from 1800 to 2021. Our proposed Scientific X-ray reproduces how an idea evolves from the very original target publication all the way to the up to date status via an extracted ‘idea tree’ that attempts to preserve the most representative idea flow structure underneath each citation network. Interestingly, we observe that while the citation counts of publications may increase unlimitedly, the maximum valid idea inheritance of those target publications, i.e., the valid depth of the idea tree, cannot exceed a limit of six hops, and the idea evolution structure of any arbitrary publication unexceptionally falls into six fixed patterns. Combined with a development potential index that we further design based on the extracted idea tree, Scientific X-ray can vividly tell how further a given idea presented by a given publication can still go from any well-established starting point. Scientific X-ray successfully identifies 40 out of 49 topics of Nobel prize as high-potential topics by their prize-winning papers in an average of nine years before the prizes are released. Various trials on articles of diverse topics also confirm the power of Scientific X-ray in digging out influential/promising ideas. Scientific X-ray is user-friendly to researchers with any level of expertise, thus providing important basis for grasping research trends, helping scientific policy-making and even promoting social development.