Are there any theories using thermodynamics/statistical mechanics or information theory principles to modelling in ecology?
John Harte's work on applying the mathematical theory of maximum entropy to ecology is certainly one of the better known examples of the application of this area of mathematics to science, in part because he literally wrote the textbook: Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford Series in Ecology and Evolution)

To be clear, maximum entropy (also known as MaxEnt in some of the literature, though most/all researchers use the longer form in publications) is a mathematical tool stemming from the fields of probability theory, statistics, and information theory.  Its use is classically most often seen in thermodynamics, statistical thermodynamics, physics, and information theory, primarily because these were the areas in which E.T. Jaynes was working when he posited the idea. Wikipedia has links to his two seminal papers.But because of it's mathematical form, it can be applied in a multitude of areas, typically where one can utilize probabilistic methods. 

If you're looking for additional areas of application, simply google the phrase "applied maximum entropy" and you'll find a wealth of areas including: econometrics, natural language processing, nuclear medicine, queuing systems, mass spectrometry, image processing, machine learning, and many others.

For ecology related work, a cross search on maximum entropy and "genetics", "evolution", "species", and similar words will provide a wealth of papers like "A maximum entropy approach to species distribution modeling".

Given the generic nature of your question, I might suggest that you'll find E.T. Jaynes' paper "On the Rationale of Maximum-Entropy Methods" (IEEE, 1982) useful.

Those generally interested in the broader applications of information theoretic methods to biology will likely appreciate some of the work that came out of last year's NIMBioS Workshop on Information and Entropy in Biological Systems (which Harte both attended and presented at), the BIRS Workshop Biological and Bio-Inspired Information Theory, and the 2014 CECAM Entropy in Biomolecular Systems. The NIMBios Workshop was organized by John Baez, a physicist, who has worked with MaxEnt methods and explored them on his blog "Azimuth".

Those with a more sophisticated mathematical background (including measure theory, functional analysis, etc.) may appreciate Henryk Gzyl's text The Method of Maximum Entropy (World Scientific: Series on Advances in Mathematics for Applied Sciences, Vol 29, 1995).

-- Additional thoughts after the question was edited -- 

First for those who don't have the background, I highly recommend reading the two seminal papers on information theory and statistical mechanics by ET Jaynes and the standard text on information theory Elements of Information Theory by Thomas M. Cover and Joy A. Thomas.

In addition to the information theoretic related areas, you might want to take a look at the discipline of complexity theory, which has primarily grown out of the Santa Fe Institute over the past several decades and which includes information theory as part of its disciplines. If you're unfamiliar with the broader topic, Melanie Mitchell has an excellent overview with her book Complexity: A Guided Tour. Also related to complexity is the area of cellular automata which one could view as a very base model of more complex ecological systems. Here, perhaps Stephen Wolfram's A New Kind of Science or Cellular Automata and Complexity will be enlightening. The broader theories coming out of these primarily mathematical areas may be useful to you.

In particular, given the types of models in ecosystems, I might suggest taking a look at some of the mathematical modeling going on at the intersection of complexity and economics. For a relatively simple introduction to this area, one could look at the relatively introductory text Complexity and the Economy by W. Brian Arthur which is very interesting. The economy is essentially a very specific type of ecology dealing with human beings, assets, and the monetary system.

Another area which I've seen a lot of literature over the last few years is applicable to the ideas of resiliency and complexity in cities, for assisting in designing more robust city planning. This really isn't that far from the naturally evolving systems being looked at in ecology settings.

For those looking for researchers in the area of complexity, I have a list of many who are on twitter in a variety of sub-areas. In addition to individuals, it also includes a number of institutes and related organizations as well.

I'd also suggest, that for the broadest theoretical setting, one could actually start with the topic known as "Big History" which takes the broadest approach of looking at history and the evolution of the cosmos over 13.7 billion years since the big bang. This conceptualization includes ideas like evolution, complexity, and emergence on the biggest scales, a set of theories that could be similarly applied to ecologies both large and small. For this viewpoint, I would suggest two works by David Christian including Maps of Time: An Introduction to Big History and Big History: The Big Bang, Life on Earth, and the Rise of Humanity.

In essence, with many of these topics and viewpoints, one is treating individual animals or even entire species as elementary particles and then using the mathematical models of statistical thermodynamics to tease out specific types of data or trends. As layers of overlapping "particles" interact with each other, they cause emergent types properties, and then these resultant emergent properties combine to create further layers of emergent properties, none of which might have been necessarily deduced from the initial conditions. Within Big History, these types of emergence go from the big bang and basic particles in the early universe to the ultimate evolution of humankind by way of a variety of stages.