Quantifying Knowledge Production Efficiency with Thermodynamics: A Data Driven Study of Scientific Concepts

We present a data-driven thermodynamic framework for analyzing how scientific concepts evolve as open, non-equilibrium systems coupled to an informational environment. Each concept is modeled as a grand-canonical ensemble whose empirical frequency distribution follows a generalized Boltzmann form derived from the Maximum Entropy principle. Using large-scale data from more than 500,000 physics papers (about 13,000 concepts, 2000–2018), we reconstruct temporal trajectories of key thermodynamic observables such as temperature, entropy, free energy, and residual entropy, and identify three characteristic regimes of concept dynamics: stochastic, non-equilibrium, and equilibrium. The analysis reveals an empirical stability plateau in the ratio between entropy and effective information energy, with mature concepts clustering around a characteristic value. This behaviour reflects a finite-size scaling constraint on the accessible informational phase space, and marks the transition to a buffered regime in which entropy production and information dissipation become balanced. In this regime, well-established concepts behave as effective thermodynamic reservoirs that stabilize the informational environment of their field. Using the Hatano–Sasa decomposition of irreversible work, we introduce efficiency measures that separate steady maintenance dissipation from adaptive reorganization costs. Together, these quantities provide a unified, thermodynamically consistent description of how scientific concepts emerge, stabilize, and reorganize under finite informational capacity, offering new insight into the statistical mechanics of knowledge production.