Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space

Abstract

Two testable schemes for quantum heat engines are investigated under the quantization framework of noncommutative (NC) quantum mechanics (QM). By identifying the phenomenological connection between the phase-space NC driving parameters and an effective external magnetic field, the NC effects on the efficiency coefficient, N , of quantum engines can be quantified for two different cycles: an isomagnetic one and an isoenergetic one. In addition, paying a special attention to the quantum Carnot cycle, one notices that the inclusion of NC effects does not affect the maximal (Carnot) efficiency, N C , ratifying the robustness of the second law of thermodynamics.

Noncommutative phase-space effects in thermal diffusion of Gaussian states

“…where θ ij and ζ ij are invertible antisymmetric real constant (d × d) matrices, and one can define the matrix Σ ij = δ ij + θ ik ζ kj / 2 , which is also invertible if θ ik ξ kj = − 2 δ ij . Writing θ ij = θ ij and ζ ij = ζ ij , with ii = 0, ij = − ji , one can interpret η and ζ as being new constants in the quantum theory, which have been extensively studied recently [13,20,[23][24][25][26]. Furthermore, there is a way of connecting the Hilbert space of the NCQM to that of the SQM, which is represented by the following relations,…”

“…It can be observed that for systems described by Hamiltonians at most quadratic in their coordinates, the noncommutative effects can be effectively mapped to the * jonas.floriano@ufabc.edu.br standard quantum mechanics as an external magnetic field acting on the system [13,[18][19][20]. This fact allows to obtain a convenient correspondence between the NCQM and the standard quantum mechanics (SQM) which is suitable to investigate how NC effects could impact some particular dynamics.…”

Isoenergetic Cycle for the Quantum Rabi Model

“…These conditions yield ξ 2 as a function of ξ 1 , and ξ 4 as a function of ξ 3 ; and are referred to as the isoenergetic condition. For a two-level system, the energy exchange along the isoenergetic process for maximal expansion given by [10,11]…”

“…[6], who envisioned the replacement of the heat baths for so-called "energy baths". This was originally presented as a proposal for the substitution of the concept of temperature with the expectation value of the system Hamiltonian [7][8][9][10]. When the system is coupled to an energy bath it evolves through an isoenergetic process during which the expectation value of the Hamiltonian is constant.…”

Quantum Mechanical Engine for the Quantum Rabi Model

“…When the system is coupled to an energy bath it evolves through an isoenergetic process, during which the expectation value of the Hamiltonian is constant. This cycle has been mostly considered for a single non-relativistic confined particle [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ], and its optimization has also been a focus of study [ 21 , 22 , 23 ]. Recently, it was extended to the case of relativistic regime by considering the single-particle Dirac spectrum [ 24 , 25 ] and has also been extended to multilevel systems [ 26 , 27 ].…”