Thermoshape effects

When two structures made by the same material and having the same sizes but different shapes are connected to each other under a temperature gradient, an electrochemical potential gradient is induced. This new effect is proposed by NERG and called quantum thermoshape effect. It can be utilized as a new way of converting heat energy to electricity.

Quantum shape effects on thermodynamics

It is shown that size-preserved shape transformations cause changes in thermodynamic properties due to wave nature of particles and it is called Quantum Shape Effects (QShE). A purely quantum mechanical torque effect appear due to QShE.

Overlapped quantum boundary layer approach

Overlapped quantum boundary layer (OQBL) approach is proposed to analytically predict QShE on thermodynamic properties. By using OQBL approach, there is no need to solve Schrödinger equation and to calculate partition function; calculation of thermodynamic properties of confined systems becomes just a simple geometrical problem.

A phase diagram for quantum oscillations

Half-vicinity model is developed and a phase diagram in degeneracy-confinement space is proposed for quantum oscillations in strongly confined and degenerate Fermi gases.

Thermosize effects

When nano and macro structures made by the same material are connected to each other under a temperature gradient, thermosize effects appear.

Quantum boundary layer

Density distribution of ideal gases confined in a finite domain is not uniform even in thermodynamic equilibrium.

Discrete Thermodynamics

Particle number and internal energy exhibit an intrinsic discreteness which allows them to take only some definite values. Thermodynamic properties of an ideal Fermi gas have either stepwise or oscillatory nature.

Quantum force

Even an infinitesimally thin wall immersed in a domain filled by a gas, has a nonzero effective thickness. Gas pressure acting on the effective cross section of movable wall causes an outward quantum force.

Dimensional Transitions

Dimensional transitions in thermodynamic properties occur in momentum space due to quantum confinement.


We derive analytical expressions for thermodynamic state functions considering quantum size and shape effects.

Nanoscale thermoelectrics

Analytical expressions for Seebeck coefficient under quantum size effects are derived with a good agreement with experimental and numerical results.

Nanoscale gas transport

Size dependencies of thermal and electrical conductivities are different, the Lorenz number becomes size and shape dependent and deviations from the Wiedemann–Franz law is expected at nanoscale due to QSE.