Prigogine showed that ordered structures can arise even far from thermal equilibrium, coining the term “dissipative structures.” In oscillating reactions such as the Belousov–Zhabotinsky system, heat flows outward so that periodic patterns persist. He introduced the concept of entropy production rate and formulated stability conditions for irreversible processes. The theory helps explain how living organisms keep their shape while metabolizing, and it is applied in chemical engineering and weather-pattern modeling.

Classical thermodynamics was limited to linear responses near equilibrium, but Prigogine extended it to include self-organization in far-from-equilibrium systems. To analyze asymmetric diffusion and autocatalytic reactions he proposed the “Brusselator,” a minimal model that exhibits temporal patterns via Hopf bifurcation. He demonstrated that when detailed balance is broken, dissipation can actually promote order rather than destroy it. These insights have been verified in ion pumps across biological membranes, convective cells in planetary atmospheres, and mode locking in semiconductor lasers—examples of nonlinear open systems. Prigogine’s work laid the foundation for complexity studies across chemistry, physics, biology, and even the social sciences.

Prigogine transcended Onsager reciprocity by applying eigenvalue analysis and variational principles to diffusion-coupled nonlinear chemical networks, deriving dynamical ordering criteria. In prototype models such as the Brusselator and Oregonator he showed that positive feedback, together with external dissipation, cooperates via a phase-transition-like mechanism to generate spatiotemporal waves. His dissipative-structure theory replaces the traditional minimum-energy principle with the idea that constrained maximization of total entropy production yields stable solutions. Using coarse-grained master equations he also sketched a precursor to modern fluctuation theorems. These achievements underpin contemporary nonequilibrium statistical mechanics, pattern selection in reaction–diffusion systems, and bifurcation analysis in nonlinear control, with applications ranging from self-oscillating devices to chronobiological rhythms.