  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.
