Quantum shape effects and novel thermodynamic behaviors at nanoscale

Abstract

Thermodynamic properties of confined systems depend on sizes of the confinement domain due to quantum nature of particles. Here we show that shape also enters as a control parameter on thermodynamic state functions. By considering specially designed confinement domains, we separate the influences of quantum size and shape effects from each other and demonstrate how shape effects alone modify Helmholtz free energy, entropy and internal energy of a confined system. We propose an overlapped quantum boundary layer method to analytically predict quantum shape effects without even solving Schrödinger equation or invoking any other mathematical tools. Thereby we reduce a thermodynamic problem into a simple geometric one and reveal the profound link between geometry and thermodynamics. We report also a torque due to quantum shape effects. Furthermore, we introduce isoformal, shape preserving, process which opens the possibility of a new generation of thermodynamic cycles operating at nanoscale with unique features. arXiv:1807.02415v1 [cond-mat.mes-hall]

Landauer’s Principle in a Quantum Szilard Engine without Maxwell’s Demon

“…Hence, their difference gives in or limits. This strong confinement behavior of is due to quantum shape effects [ 48 ] and it will not change the arguments for the resolution of the Szilard engine problem in this work. The quantum shape effects on thermodynamic processes of strongly confined systems will be the subject of another study.…”

“…Free energy slowly changes during the initial entrance of the partition, because of the less probability density between and nm due to QBL near container’s boundaries. Then, free energy linearly increases during the insertion until around nm where QBLs of partition and the container wall starts to overlap [ 48 ] in which free energy saturates to its final value at nm. Free energy variation is approximately equal to the effective pressure times the effective thickness which corresponds to the quantum force exerted on the partition with zero thickness [ 47 ].…”

“…They perfectly match with the expressions given by Equations (7)–(9), that is why we did not plot them in Figure 4 . The relative errors are less than even for nm at K. For even stronger confinements, one needs to consider quantum shape effects [ 48 ] as well in order to get even more accurate representations, but for our analysis here, the analytical expressions given in Appendix A are quite sufficient.…”

Entropy Distribution in a Quantum Informational Circuit of Tunable Szilard Engines

“…7, that denotes the probability for the particle to end in the left compartment when the wall is removed and slowly reintroduced at position . The saturation elbows are quantum effects that are explained physically in References [66,67].…”

Heat kernel approach for confined quantum gas

“…The thermodynamic properties of gases in confined space have been widely investigated in recent years, including classical gases [11][12][13] and quantum gases [14][15][16]. Many studies show that in confined space, ideal gases will show non-uniform [17,18] or anisotropy [19] due to the existence of the boundary. In addition, the studies on the influence of boundary to ideal gases lead to some other progresses.…”