English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Similarly to the derivation of the Gibbs-Boltzmann distribution forstructureless indistinguishable particles, we consider multi-particle systemssome of which are contained (or delimited) inside others (Problem 1), as wellas systems of particles delimited within other particles, which, in turn, aredelimited yet inside another kind of particles (Problem 2). Under the naturalassumptions concerning the conservation laws, such as the conservation of thetotal number of particles, total energy, etc, the problem of the most probableenergy distributions is studied in a combinatorial formulation, with theobtained distributions treated as externally observable. For Problem 1, theparticle distributions over maximal and minimal energies are also establishedand shown to coincide with the ones found in the framework of the originalcombinatorial treatment. The results for Problems 1 and 2 can be interpreted asa sorting of lower-level particles based on their statistical mechanicsbehavior observed in various experiments. An effective Pauli principle arisesin a non-contradictory manner in one-particle observations for the completeprobabilistic Problem 1 in the combinatorial formulation as well as in theproblem of distributions over maximal and minimal energies. Several of thecalculated distributions describe particles having no negative energy states.

Most Probable Energy Distributions of Particles with Hierarchial Structures