Editing Concave function (section)

==Applications==
* Rays bending in the [[computation of radiowave attenuation in the atmosphere]] involve concave functions.
* In [[expected utility]] theory for [[choice under uncertainty]], [[cardinal utility]] functions of [[risk aversion|risk averse]] decision makers are concave. 
* In [[microeconomic theory]], [[production function]]s are usually assumed to be concave over some or all of their domains, resulting in [[diminishing returns]] to input factors.<ref>{{cite book |first1=Malcolm |last1=Pemberton |first2=Nicholas |last2=Rau |title=Mathematics for Economists: An Introductory Textbook |publisher=Oxford University Press |year=2015 |isbn=978-1-78499-148-7 |pages=363–364 |url=https://books.google.com/books?id=9j5_DQAAQBAJ&pg=PA363 }}</ref>
* In [[thermodynamics]] and [[information theory]], [[Entropy (information theory)|entropy]] is a concave function. In the case of thermodynamic entropy, without phase transition, entropy as a function of extensive variables is strictly concave. If the system can undergo phase transition, and if it is allowed to split into two subsystems of different phase ([[phase separation]], e.g. boiling), the entropy-maximal parameters of the subsystems will result in a combined entropy precisely on the straight line between the two phases. This means that the "effective entropy" of a system with phase transition is the [[convex envelope]] of entropy without phase separation; therefore, the entropy of a system including phase separation will be non-strictly concave.<ref>{{Cite book |last1=Callen |first1=Herbert B. |title=Thermodynamics and an introduction to thermostatistics |last2=Callen |first2=Herbert B. |date=1985 |publisher=Wiley |isbn=978-0-471-86256-7 |edition=2nd |location=New York |pages=203–206 |chapter=8.1: Intrinsic Stability of Thermodynamic Systems}}</ref>