2013/10/23 by Luís F. Seoane, Ricard V. Solé, Seoane, Luís F. +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Microbial Metabolic Engineering and Bioproduction #Phase Equilibria and Thermodynamics #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1310.6372
openalex publication_date 2013/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions involve a compromise between both. The theory of Pareto (or multi objective) optimization provides a general framework to explore these problems and find the space of possible solutions compatible with the underlying tradeoffs, known as the \em Pareto front. Conflicts between constraints can lead to complex landscapes of Pareto optimal solutions with interesting implications in economy, engineering, or evolutionary biology. Despite their disparate nature, here we show how the structure of the Pareto front uncovers profound universal features that can be understood in the context of thermodynamics. In particular, our study reveals that different fronts are connected to different classes of phase transitions, which we can define robustly, along with critical points and thermodynamic potentials. These equivalences are illustrated with classic thermodynamic examples.