The following paper develops a relationship between statistical mechanics and concentration inequalities.  Derivations based on this relationship are
given for a variety of standard inequalities.

<p><a href = https://scholar.google.com/citations?view_op=view_citation&hl=en&user=nbpafUkAAAAJ&cstart=60&citation_for_view=nbpafUkAAAAJ:NMxIlDl6LWMC>
Concentration inequalities for the missing mass and for histogram rule error</a> with Luis Ortiz, Journal of Artificial Intelligence Research (JAIR) 2003.</p>

While the above paper failed to convincely demonstrate the value of the connection between statistical mechanics and concentration,
Andreas Maurer was able to use the connection much more convincingly in later papers.  See for example <a href = https://arxiv.org/pdf/1205.1595.pdf> Thermodynamics and Concentration</a>.