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Quantum Shape Effects

Can we change the shape of a domain without altering its sizes? By introducing a size-invariant shape transformation, we propose the existence and explore the consequences of a new type of physical effect appearing at the quantum scales, which we call here as "quantum shape effect". By completely separating the shape effects from size effects, we show that shape alone becomes a control parameter on the thermodynamic state functions of confined systems at nanoscale. We develop an overlapped quantum boundary layer method to analytically predict the quantum shape effects, reducing a thermodynamic problem into a geometric one and revealing the profound link between the geometry and thermodynamics at the quantum scales. Furthermore, we introduce the isoformal, shape preserving, process which opens up the possibility of a new generation of thermodynamic cycles operating at nanoscale with unique features. As a whole, this thesis constitutes the proposition and a comprehensive investigation of the theory, construction of the methodology and exploration of the applications of quantum shape effects in thermodynamics.