Creation and annihilation operators, for example, are not self-adjoint but they do correspond to changes in particle number in multi-particle states.
42.
Elements of a Fock space which are superpositions of states of differing particle number ( and thus not eigenstates of the number operator ) are not Fock states.
43.
The state of a thermodynamic system is specified by a number of volume, internal energy, and the amount of each constituent particle ( particle numbers ).
44.
For example, in the canonical ensemble the number of particles inside the system is held fixed, whereas particle number can fluctuate in the grand canonical ensemble.
45.
As of September 2017, Euro 6 emission regulations will limit particle numbers at a maximum of 6 x 10 11 per kilometre over the New European Driving Cycle.
46.
For a simple system in which the particle numbers are constant, the second derivatives of the thermodynamic potentials can all be expressed in terms of only three material properties
47.
Here, the temperature, pressure, and chemical potential are the generalized forces, which drive the generalized changes in entropy, volume, and particle number respectively.
48.
This is due in part to the fact that, given the same mass per volume, the dose in terms of particle numbers increases as particle size decreases.
49.
Since the system is closed, the particle number " N " is constant and a small change in the energy of the system would be given by:
50.
For the case of the absence of matter, quantum field theory is necessary, because non-relativistic quantum mechanics with fixed particle numbers does not provide a sufficient account.
