### A Statistical-Mechanical Perspective on Site Fidelity – Part IV

In Part I of this set of posts I described animal space use from the perspective of ergodicity. This is a key concept of standard statistical mechanics, with similar importance to analysis of individual paths and home range data under the extended theoretical framework (the parallel processing conjecture, expressed by the MRW model). Below I elaborate on this theme. I indicate by simulation examples the transition from a fully ergodic state on the home range scale to a narrowing of this scale as the series of fixes become increasingly autocorrelated (higher-frequency sampling). From a biophysical perspective, the following system description may point towards my most important theoretical development since the Scaling cube. This will become clearer as I gradually turn my upcoming posts from description of statistical-mechanical properties towards how to explore these properties in novel methods for ecological inference. First consider the general principle that the transition from