The concept of entropy, originating from thermodynamics, has played a pivotal role in shaping the field of ecological economics by providing a scientific framework to understand the limits of economic processes within natural systems. Entropy, fundamentally, refers to the measure of disorder or randomness in a system and indicates the tendency of energy to disperse or degrade over time. In classical thermodynamics, the second law states that in any energy transfer, some energy becomes unavailable for work, leading to an increase in entropy. This principle highlights that natural systems are not infinitely recyclable or self-renewing without losses, which directly challenges the traditional economic assumption of endless growth and substitution of natural resources through human innovation. Traditional economics, particularly neoclassical economics, often assumes that resources are substitutable and that technological progress can indefinitely offset natural resource depletion. This assumption largely ignores the physical realities of energy and matter flows. The integration of the concept of entropy into economic thought brought a paradigm shift by emphasizing that economic activity is embedded within ecological limits. Nicholas Georgescu-Roegen, a foundational thinker in ecological economics, was particularly instrumental in applying the notion of entropy to economics. In his work, Georgescu-Roegen argued that economic processes are fundamentally unidirectional because the transformation of low-entropy resources into goods and services inevitably produces high-entropy waste. This perspective underscores the irreversibility of resource depletion and environmental degradation, contrasting sharply with the circular flow models of classical economics which implicitly treat energy and matter as indefinitely reusable. The entropy concept also illuminates the physical constraints on human economic activity. By viewing the economy as a subsystem of the