Exceptional Particles, or E-Particles in common HOTEL parlance, refers to particles that are suspicious because they do not conform to the patterns they should follow in the time or universe in which they are found. The detection of such unusual particles often indicates that odd things are afoot, and as such are often investigated by local protagonists!
Any particle or substance whose existence at a particular place or time is suspicious enough to warrant special investigation might be considered an E-Particle. Finding a treasure chest full of garnets and rubies on a 1600's treasure ship might well be expected. Finding a treasure chest on the same ship containing Kyber Crystals or Adamantium, even in nanogram quantities so miniscule to be detectable only by ultra-advanced technology, has serious implications and would almost certainly be considered E-Particles. Discovering such exceptional particles that do not conform to the laws of the universe, or traces of materials from that era's far future which have absolutely no reason to be in the ancient world might not be as overt a threat to the observer (or the web of of time) as being set upon by Scythian horsemen wielding plasma lances and bazookas in lieu of poisoned arrows, but it does overwhelmingly suggest timeline shenanigans that might need to be put right, just the same.
Type I E-Particle Example: Exceptional by Space/Time Location
Every culture throughout the multiverse tends to have its own understanding of material science. Technology level continues to progress, barring catastrophe, and different worlds and civilizations have discovered how to harness or synthesize various natural materials and exotic matter. This tends to follow discoveries, and move from the simple to to complex (stone age, copper age, bronze age, iron age, etc). Powerful space-faring and time-travelling societies, at least those who are litigious and/or ethical, typically have strict laws regarding interfering with developing cultures by giving them technology far beyond their understanding. When travelling to a specific time period or world, wise investigators keep their scanners/tricorders/screwdrivers peeled for materials or signatures that have no business being there as they strongly indicate outside contamination. E-particles in this context might be traces of Diamondium or Diamondillium before the year 3000, electromagnetic signatures in London in Restoration-Era England, or radioactive fallout detected during Abraham Lincoln's inaugural address. Each of these examples of E-Particles would almost certainly merit investigation by any protagonist time-travelers in the immediate vicinity because, no matter how small they are, they have no business being there.
Type II E-Particle Example: Exceptional by Abundance
Although the universe is made of all kinds of tiny units that get together to form atoms, molecules, and matter itself, some are more frequently encountered than others. Hydrogen and Helium are relatively common. Astatine is extremely rare. That's because even the most stable atom of Astatine has a half-life of about 8 hours. Every 8 hours, 50% of the Astatine atoms in a given group will undergo radioactive decay, becoming a different element, and releasing energy. Another half-life period, 8 hours, means that on overage only 1/4 of the Astatine atoms will remain. This means that, every day (24 hours) that passes, the earth loses about 7/8 of its supply of Astatine. Some atoms in other elements, though they have longer half-lives, are like this too--their numbers decrease over time. Humans figured this out about 100 years ago, and have been exploiting it ever since. Frederick Soddy was working with a number of chemical samples that all had different radioactive properties but similar chemical properties, and realized they were all "isotopes" of the element Thorium. Isotope, which means "same place" in Greek, refers to atoms that all have the same number or protons, but different numbers of neutrons (and since it's the protons that determine the element, they hold the "same place" on the periodic table). Once humanity learned about isotopes, which ones were stable with extremely long half-lives and unstable with short ones, they quickly began using them to date objects by the percentage of decayed-vs-undecayed atoms. Carbon-14 has a half-life of about 6000 years, and is used to determine the age of archaeological relics. Potassium-40 has a half-life of 1,248,000,000 years, and humans hold it as a useful tool to date ages on the scale of planets. As far as humanity reasoned, there might have been Plutonium when the Earth formed, but it had all decayed before December, 1940, when humanity first synthesized it--and their product was therefore the biggest sample of Plutonium on the planet. Due to the age of the Earth, certain isotopes and elements should be either exceptionally rare outside of the colliders and reactors that can briefly create the largest and most short-lived elements, and therefore not detectable outside of such locations. Concentrations of impossibly large proportions of atoms that should have decayed long ago would DEFINITELY be considered E-Particles, and heavily suggest that SOMETHING is off-base.
Confirmed Concentrations of Type II E-Particles
1) Large amounts of E-Particles have been found during investigation the other side of mysterious portals which have been popping up on the HOTEL grounds lately. Particles containing isotopes in concentrations either FAR LOWER or FAR HIGHER than would be expected of the portal's location were discovered by careful scans of events, people, footage, and equipment that was encountered during searches of strange places such as the Central Europe in 116 AD, and in Mamluk Egypt of 1324 AD. These readings suggest that at least some objects encountered were either a different age than the destinations, from another universe/timeline, or created with such high-technology that every atom used was individually selected. As this was occurring in conjunction with the confrontation with a mysterious and powerful female time-active wearing powerful future-tech armor and with red hair who was absolutely rife with these unusual E-Particles, this person was hypothesized to be connected to Simon Kerrick, whose creations spurred the first detection and naming of the term (see below).
2) Objects from Simon's demiplane of Enclave seem to have plentiful E-Particles in the form of abundant chemical isotopes that should be long gone at the age of the Earth/Universe. Objects from Simon's realm, however, apparently still contains large amounts of these comparatively rare isotopes because it was created within the last decade. Readings of unstable radioisotopes far out of the norm are thus characteristic of the Lich's creations, and so Sakura Xadium Aino, in her investigations, originally designated E-Particles after the method[Easy][Enclave]-Particles. This has been recorded on gifts from Simon and originating from Enclave that were left for Bixia Yuanjin, as well as on an incredibly mysterious and clearly supernatural key that has bonded itself to Eliza McIntash, after being passed through the hands of numerous time-actives. For the serious and absolutely hopelessly immersed academic/Time Lord/physicist, this has staggering implications about the world of Enclave and its forging, including positing the question of whether the plane's inhabitants are aware of and can cope with this markedly increased radioactivity, and calling into question if Enclave's existence could shed light on whether relative elemental isotope abundance is the same for atoms of elements created in stars, through supernovae and fusion, as it is for elements conjured with raw magical force. As Enclave has yet been unexplored, the mystery remains.