Quantum shape effects and novel thermodynamic behaviors at nanoscale

TL;DR

This paper demonstrates that the shape of nanoscale confinement domains uniquely influences thermodynamic properties through quantum effects, introducing an analytical method and new thermodynamic processes based on geometry.

Contribution

It introduces a novel analytical approach to isolate quantum shape effects and explores their impact on thermodynamics at the nanoscale, including torque and shape-preserving processes.

Findings

Shape affects Helmholtz free energy, entropy, and internal energy.

Quantum shape effects induce a torque in confined systems.

Proposes an isoformal process for nanoscale thermodynamics.

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 Schr\"odinger 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.