Computational Entropy Modeling for Sustainable Energy Systems: A Review of Numerical Techniques, Optimization Methods, and Emerging Applications

Thermodynamic entropy generation quantifies irreversibility in energy conversion processes, providing rigorous thermodynamic foundations for optimizing efficiency and sustainability in thermal and energy systems. This critical review synthesizes advances in computational entropy modeling across numerical methods, optimization strategies, and sustainable energy applications. Computational fluid dynamics, finite element methods, and lattice Boltzmann methods enable spatially resolved entropy analysis in convective, conjugate, and microscale systems, but exhibit varying maturity levels and accuracy–cost trade-offs. The minimization of entropy generation and the integration of artificial intelligence demonstrate quantifiable performance improvements in heat exchangers, renewable energy systems, and smart grids, with reported efficiency gains of 15 to 39% in specific applications under controlled conditions. While overall performance depends critically on system scale, operating regime, and baseline configuration, persistent limitations still constrain practical deployment. Systematic conflation between thermodynamic entropy (quantifying physical irreversibility) and information entropy (measuring statistical uncertainty) leads to inappropriate method selection; validation challenges arise from entropy’s status as a non-directly-measurable state function; high-order maximum entropy models achieve superior uncertainty quantification but require prohibitive computational resources; and standardized benchmarking protocols remain absent. Research fragmentation across thermodynamics, information theory, and machine learning communities limits integrated frameworks capable of addressing multi-scale, transient, multiphysics systems. This review provides structured, cross-method, application-aware synthesis identifying where computational entropy modeling achieves industrial readiness versus research-stage development, offering forward-looking insights on physics-informed machine learning, unified theoretical frameworks, and real-time entropy-aware control as critical directions for advancing sustainable energy system design.