... Historically, the fundamental principles of physics rst concerned the problems of
matterwhat things are made of and how they move. Later, the problems of energy started
to be reected in the leading principles of physicshow energy is created, expressed and
transformed. As the next stage an altern ...
... efficiency). This does not only involve putting the injected particles on to the
beam path of the machine but also involves getting these particles trapped in
the machine acceptances (transverses and longitudinal) so that they can be
stored or further accelerated.
The specific case of the cyclotro ...
Introduction to Thermodynamics and Statistical Physics
... Following Shannon [1, 2], the entropy function σ (p1 , p2 , ..., pN ) can be alternatively defined as follows:
1. σ (p1 , p2 , ..., pN ) is a continuous function of its arguments p1 , p2 , ..., pN .
2. If all probabilities are equal, namely if p1 = p2 = ... = pN = 1/N, then
the quantity Λ (N ) = σ ( ...
Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to elementary particles such as electrons, composite subatomic particles such as atomic nuclei, as well as atoms and molecules. Quasiparticles also behave in this way. Although all known indistinguishable particles are ""tiny"", there is no exhaustive list of all possible sorts of particles nor a clear-cut limit of applicability; see particle statistics #Quantum statistics for detailed explication.There are two main categories of identical particles: bosons, which can share quantum states, and fermions, which do not share quantum states due to the Pauli exclusion principle. Examples of bosons are photons, gluons, phonons, helium-4 nuclei and all mesons. Examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei.The fact that particles can be identical has important consequences in statistical mechanics. Calculations in statistical mechanics rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behavior from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.