Quantum Advantage of Thermal Machines with Bose and Fermi Gases

Abstract

In this article, we show that a quantum gas, a collection of massive, non-interacting, indistinguishable quantum particles, can be realized as a thermodynamic machine as an artifact of energy quantization and, hence, bears no classical analog. Such a thermodynamic machine depends on the statistics of the particles, the chemical potential, and the spatial dimension of the system. Our detailed analysis demonstrates the fundamental features of quantum Stirling cycles, from the viewpoint of particle statistics and system dimensions, that helps us to realize desired quantum heat engines and refrigerators by exploiting the role of quantum statistical mechanics. In particular, a clear distinction between the behavior of a Fermi gas and a Bose gas is observed in one dimension, rather than in higher dimensions, solely due to the innate differences in their particle statistics indicating the conspicuous role of a quantum thermodynamic signature in lower dimensions.

Study of quantum Szilard engine for non-interacting bosons in fractional power-law potentials

“…For a single-particle, there is double degeneracy in the quantized energy levels if a single barrier is inserted isothermally [4,15,22]. For N non-interacting indistinguishable particles there will be 2 N degeneracy in the combined partition function when in boxes B and C of figure 1 [14].…”

“…In the Stirlinglike cycle in figure 1, the system (a single-particle) is coupled to the hot bath of temperature T h when the particles are in boxes A and B. Similarly, the system is coupled to the cold bath of temperature T c when the particles are in boxes C and D [4,14,29]. Therefore from figure 1, heat is supplied to the system via the processes (2) and (3), and heat is absorbed from the system via the processes (1) and (4) [14].…”

“…Similarly, the system is coupled to the cold bath of temperature T c when the particles are in boxes C and D [4,14,29]. Therefore from figure 1, heat is supplied to the system via the processes (2) and (3), and heat is absorbed from the system via the processes (1) and (4) [14]. The processes (1) and (3) are isothermal expansion and compression and processes (2) and (4) are isochoric processes [4,14,29].…”

“…However it may be worth noting that general guidance is provided in modern formulations of the problem, very general and fully-quantum frameworks for Szilard-Landauer type analyses without any limitations to single particles or particular potentials [12,13]. In the classical limit, the insertion and removal of the barrier do not cost an extra amount of work [14,15]. However this is not true in the quantum regime because the insertion of the barrier shifts the energy eigenvalues [4,5,[16][17][18][19][20].…”

“…We have shown that the efficiency increases with the increase in the particle number for non-interacting bosons in fractional power-law potential. The maximum efficiency is however restricted by the Carnot efficiency [14,15,22,24]. Since the non-interacting bosons partition function has a dependency on the chemical potential explicitly, the extraction of positive non-zero work and hence efficiency is only possible for the converging nature of the grand partition function.…”