Thermodynamics seems to be simple for homogenous infinite systems

• + Sharp phase transitions (Singularity of specific heat)
• + Gibbs-Duhem Relation
• - No Hilbert Space for QM of System
• - No experimental system known (World is finite)

Thermodynamics is tricky for finite systems

• - Infinitely more Variables: volume, shape-, surface-moments, of matter, charge, magnetization distribution, particle number
• - Problem of Self-adjustment: reduction of no. of independent variables
• - Problem of definition of phase transitions: smooth specific heat curves, pp.
• - Problem of numerical complexity and computation time
• - Problem of experimental verification
• - Problem of discrete particle numbers.

Now the good news for Thermodynamics of small systems

• Hilbert space for QM
• From Diff.Equ. to Path Integral computation: calculation time proportional to particle number power
• Shell effects
• Thermodynamics of two variables (e.g. B, T)
• Unique definition of phase transition
• Recursion Relations
• Scattering usable for specific heat
• Experiments for different T can be added.
• Quantum statistics can be treated correctly for finite number of particles

A Comment to Science Progress

Presentation of the Group's results to other physicists

• All papers are online back to 1967
• Group home page
• personal homepages