Making Sense of the Legendre Transform Export

@misc{citeulike:2906302, abstract = {The Legendre Transform (LT) is a common feature of many upper division and graduate physics classes. However, discussions of it tend to be ad hoc, poorly motivated, and confusing. As a result, the LT equations become something to be memorized without understanding. In this paper we describe a more satisfying way of looking at LT relations both mathematically and physically. Mathematically this results in highly symmetric equations that clarify the structure of the transform both algebraically and geometrically. Physically, we motivate the transform as an issue of choosing independent variables that are easily controlled and give examples drawn from classical mechanics and thermodynamics. In thermodynamics, we demonstrate how the LT arising naturally from statistical mechanics and show how use of dimensionless thermodynamic potentials lead to more natural and symmetric relations.}, archivePrefix = {arXiv}, author = {Zia, R. K. P. and Redish, Edward F. and Mckay, Susan R.}, citeulike-article-id = {2906302}, citeulike-linkout-0 = {http://arxiv.org/abs/0806.1147}, citeulike-linkout-1 = {http://arxiv.org/pdf/0806.1147}, eprint = {0806.1147}, keywords = {classical\_mechanics, legendre\_transform, statistical\_mechanics, thermodynamics}, month = {Jun}, posted-at = {2009-03-08 10:45:58}, priority = {2}, title = {Making Sense of the Legendre Transform}, url = {http://arxiv.org/abs/0806.1147}, year = {2008} }

TY - ELEC ID - citeulike:2906302 L3 - citeulike-article-id:2906302 N2 - The Legendre Transform (LT) is a common feature of many upper division and graduate physics classes. However, discussions of it tend to be ad hoc, poorly motivated, and confusing. As a result, the LT equations become something to be memorized without understanding. In this paper we describe a more satisfying way of looking at LT relations both mathematically and physically. Mathematically this results in highly symmetric equations that clarify the structure of the transform both algebraically and geometrically. Physically, we motivate the transform as an issue of choosing independent variables that are easily controlled and give examples drawn from classical mechanics and thermodynamics. In thermodynamics, we demonstrate how the LT arising naturally from statistical mechanics and show how use of dimensionless thermodynamic potentials lead to more natural and symmetric relations. TI - Making Sense of the Legendre Transform KW - classical_mechanics KW - legendre_transform KW - statistical_mechanics KW - thermodynamics AU - Zia, RKP AU - Redish, Edward AU - Mckay, Susan PY - 2008/Jun/06/ UR - http://arxiv.org/abs/0806.1147 ER -