Second law of thermodynamics
The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent.
Sustainability metrics and indices
University of Maryland School of Public Policy professor and former Chief Economist for the World Bank Herman E. Daly (working from theory initially developed by Romanian economist Nicholas Georgescu-Roegen and laid out in his 1971 opus "The Entropy Law and the Economic Process") suggests the following three operational rules defining the condition of ecological (thermodynamic) sustainability:Some commentators have argued that the "Daly Rules", being based on ecological theory and the Laws of Thermodynamics, should perhaps be considered implicit or foundational for the many other systems that are advocated, and are thus the most straightforward system for operationalization of the Bruntland Definition. In this view, the Bruntland Definition and the Daly Rules can be seen as complementary—Bruntland provides the ethical goal of non-depletion of natural capital, Daly details parsimoniously how this ethic is operationalized in physical terms. The system is rationally complete, and in agreement with physical laws. Other definitions may thus be superfluous, or mere glosses on the immutable thermodynamic reality.