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We evaluate quantum Otto, Diesel and Brayton cycles employing
multiple-state 1D box system instead of ideal gas filled cylinder. The work and
heat are extracted using the change in the expectation of Hamiltonian of the
system which leads to the first law of thermodynamics to quantum system. The
first law makes available to redefine the force which is in fact not well
defined in a quantum mechanical system and then it is applied to define the
quantum version of thermodynamic processes, i.e.
isobaric, isovolume and adiabatic. As the results, the efficiency of quantum
Otto engine depends only on the compression ratio and will be higher than the
efficiency of quantum Diesel which can decrease by the widening of expansion
under isobaric process. The efficiency of quantum Brayton engine may reach
maximum on certain combination between the wide of box under isobaric expansion
and compression, under certain conditions. The amount of levels participated in
the quantum heat engine system will potentially reduce the performance of the
quantum heat cycles consisting isobaric process, but it can be resisted using
isobaric process controller.
We want to show extra-dimensions corrections for Fermionic Casimir Effect. Firstly, we determined quantization fermion field in Three dimensional Box. Then we calculated the Casimir energy for massless fermionic field confined inside a three-dimensional rectangular box with one compact extra-dimension. We use the MIT bag model boundary condition for the confinement and M4 × S1 as the background spacetime. We use the direct mode summation method along with the Abel-Plana formula to compute the Casimir energy. We show analytically the extra-dimension corrections to the Fermionic Casimir effect to forward a new method of exploring the existence of the extra dimensions of the universe.