thought experiment nevertheless described a fundamental limit of nature. As kinetic theory replaced caloric theory through the early and mid-19th century (see Timeline of thermodynamics), several scientists added mathematical precision to the first and second laws of thermodynamics and developed the concept of entropy. Carnot's focus on processes at the human scale (above the thermodynamic limit) led to the most universally applicable concepts in physics. Entropy and the second-law are applied today in fields ranging from quantum mechanics to physical cosmology. Gibbs In the 1870s, Josiah Willard Gibbs unified a large quantity of 19th century thermochemistry into one compact theory. Gibbs's theory incorporated the new concept of a chemical potential to cause change when distant from a chemical equilibrium into the older work begun by Carnot in describing thermal and mechanical equilibrium and their potentials for change. Gibbs's unifying theory resulted in the thermodynamic potential state functions describing differences from thermodynamic equilibrium. In 1873, Gibbs derived the mathematics of "available energy of the body and medium" into the form it has today. (See the equations above). The physics describing exergy has changed little since that time. Helmholtz In the 1880s, German scientist Herman Von Helmholtz derived the equation for the maximum work which can be reversibly obtained from a closed system. Rant In 1956, Yugoslav scholar Zoran Rant proposed the concept of Exergy, extending Gibbs and Helmholtz' work. Since then, continuous development in exergy analysis has seen many applications in thermodynamics, and exergy has been accepted as the maximum theoretical useful work which can be obtained from a system with respect to its environment. See also Thermodynamic free energy Entropy production Energy: world resources and consumption Emergy Notes References Further reading Stephen Jay Kline (1999). The Low-Down on Entropy and Interpretive Thermodynamics, La Cañada, CA: DCW Industries. . External links Energy, Incorporating Exergy, An International Journal An Annotated Bibliography of Exergy/Availability Exergy – a useful concept by Göran Wall Exergetics textbook for self-study by Göran Wall Exergy by Isidoro Martinez Exergy calculator by The Exergoecology Portal Global Exergy Resource Chart Guidebook to IEA ECBCS Annex 37, Low Exergy Systems for Heating and Cooling of Buildings Introduction to the Concept of Exergy Thermodynamic free energy State functions Ecological economics