|The 2009 Dictionary of Energy definition of emergy by Mark Brown. |
The concept of emergy seems to be a type of verbal energy flow concept, similar to the concept of transformations of energy in the steps of the food chain, albeit with an ecological-economic focus.
There isn't really anything that is "thermodynamic" about the concept of emergy; although the term is often found mixed up in thermodynamics discussions, such as terms including "available energy" (a Willard Gibbs' term for free energy), exergy, among others. The term seems to be a type of verbal thermodynamics.
The term “emergy” was coined in the late 1980s by Australian David Scienceman, while working as a visiting scientist at Howard Odum’s research group at the University of Florida, and supposedly was introduced to be a replacement to Odum’s term “embodied energy”, which had been used to refer to energy quality differences in terms of their costs of generation, and a ratio called a “quality factor” for the calories (or joules) of one kind of energy required to make those of another. 
In these years a terminology overlap resulted since the term embodied energy was being used by other groups who were evaluating the fossil fuel energy required to generate products and were not including all energies or using the concept to imply quality, embodied energy was dropped in favor of “embodied solar calories” and the quality factors became known as "transformation ratios".
The term "embodied energy", supposedly, was abandoned altogether in 1986 when David Scienceman, a visiting scholar at the University of Florida from Australia, suggested the term “emergy” and "emjoule" or "emcalorie" as the unit of measure to distinguish emergy units from units of available energy.
The term transformation ratio was shortened to transformity in about the same time; and is said to be defined as the ratio of total emergy input to the available energy of the product. 
The term "emergy" was employed by Odum and later used theoretically, in ecological thermodynamics, by those including: Eugene Odum, Sven Jorgensen, and Marlan Blissett.
1. Flournoy, Alyson C. and Driesen, David M. (2010). Beyond Environmental Law (pg. 105). Cambridge University Press.
2. Cleveland, Cutler J. and Morris, Christopher G. (2009). Dictionary of Energy (section: emergy, pg. 163). Elsevier.
3. David M. Scienceman – Wikipedia.
● Wayburn, Thomas L. (1993). “Thermodynamics, Availability, and Emergy”, Dematerialism.net.
● Emergy – Wikipedia.