Quantifying Knowledge Evolution With Thermodynamics: A Data-Driven Study of Scientific Concepts

In this work, we propose a thermodynamic framework to analyze the creative potential of scientific fields by examining over 11,000 scientific concepts across 500,000 publications from ArXiv (2002-2018). Our approach demonstrates that scientific concepts' term frequencies (tf) follow a generalized Boltzmann distribution, enabling a rigorous thermodynamic description. We compute key thermodynamic properties of scientific concepts, treating them as closed thermodynamic systems. The observed most probable temperature, T≃3/2, corresponds to the maximum concept heat capacity, indicating a phase transition from non-equilibrium states with a linear energy spectrum to stable stationary states characterized by logarithmic energy spectra and power-law distributions of tf. Concepts typically reach these stable states after being referenced in over 1,000 documents. The thermodynamic state space of scientific concepts is analyzed using data-driven diagrams, revealing correlations between energy, temperature, entropy, free energy, and residual entropy, which govern information transfer between concepts.