Our neighborhood “wild” turkeys like to visit our birdbath — one of their favorite watering spots. Occasionally they will actually try to bathe in it, like the little birds. This mostly just makes a wet feathery mess of things 😂
#wildlife
#birds
#wildturkey
![\textbf{2.4.3 Ensemble Averaging}
\noindent The far-reaching significance of ensemble averaging was cemented in physics by the work of \textcolor{blue}{Gibbs (1902)}. As \textcolor{blue}{Kittel (1958)} notes, ``the scheme introduced by Gibbs... [provides a formal way] to replace \textit{time averages} over a single system by \textit{ensemble} averages, which are averages at a fixed time over all systems in an ensemble.'' With specific reference to the statistical mechanics of gas particles, \textcolor{blue}{Gibbs (1902)} defined an ensemble as ``a great number of independent systems, identical in nature, but differing in phase, that is, in their condition with respect to configuration and velocity.'' For context we briefly outline below the concept of a Gibbs ensemble in relation to gas particles, and then develop this concept more fully in Chapter 9. A key point of this section is to illustrate that the concept of a Gibbs ensemble as applied in stochastic systems analysis is now much broader than what Gibbs originally envisioned, owing to the clear interpretive value of ensemble averaging. For our purposes we may define a Gibbs-like ensemble as a great number of independent but nominally identical systems, each evolving independently but in the same probabilistic manner.
In appealing to a Gibbs-like ensemble, we often are referring to a set of imagined systems that are nominally identical to a real prototype system. In this case the number of imagined systems may be arbitrarily large. In certain situations, as outlined in examples below, we can identify an ensemble consisting of real systems, although the ensemble size might be small relative to an imagined large ensemble. Nonetheless, this situation lends realism to the idea of an \textit{ensemble distribution} and ensemble averaging.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:6ui77txzzc5prhvlfcvrzqqb/bafkreibtnnu62zwtzoiub3vi3kdvsgz6v4hwxzn4tpuy4t7wwp5jzwkyqm)
![Moreover, the ingredients of [expressions of the soil particle flux] are in principle well defined, and the simple linear forms of these expressions appear to hold no surprises. Stated another way, rain splash transport is perhaps the ``tamest'' surface transport process imaginable --- the ``simplest of all geomorphic processes'' (Dunne et al., 2010, p. 15). It is therefore an ideal example to examine the probabilistic consequences of rarefied transport conditions for comparison with a conventional deterministic (continuum-like) description of a process that is fundamentally noise driven. Indeed, like the process of radioactive decay and its measurement, an explanation of rain splash transport requires a probabilistic description; no other possibility exists.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:6ui77txzzc5prhvlfcvrzqqb/bafkreic666ymnq4kvpnyfh5bysloa5fxb3g3mjk4pihdm5a5nqkh5rhggq)
