Dynamical Systems, Markov Chains, Information Theory and Statistical Mechanics.
Energy and Entropy seems like a very profound concepts applicable to many different kind of situations. In the book Nonlinear Dynamics by Strogatz I saw that in continuos dynamical systems, stable fixed points can be seen local minima in a potential well through some transformation. Leonard Susskind's statistical mechanics class on youtube starts very nice showing a sort of markov chain with transitions of probability 1 to illustrate the concept of entropy.
All these topics seem to be profoundly connected, but historically they have been developed by different scientific communities. Are there introductory texts that try to consolidate them?
You might try "Thermodynamics of Chaotic Systems: An Introduction" by Christian Beck and Friedrich Schögl.
A classic foundational text is ET Jaynes, Probability Theory: The Logic of Science. Jaynes presents information theory from a physicist's perspective which includes solid fundamental introductions to MaxEnt Markov Methods, how information theory relates to classical statistical science, etc. It is a bit dated, but it is a solid book and is often referenced in scholarly articles about this subject. If you are going to employ information theory and statistical mechanics in your research modeling, this book will provide you with a solid grounding that is shared by most researchers using these methods.
This site can help.
http://www.albany.edu/physics/acaticha.shtml
Ariel Caticha working on these issues.
The book of MacKay, "Information Theory, Inference and Learning Algorithms"
http://www.amazon.com/Information-Theory-Inference-Learning-Algorithms/dp/0521642981
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
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