# Is there a non-information theoretic justification of the maximization principle of entropy?

All modern derivations of statistical quantum mechanics I've found in the literature, have relied on the axiom, that the physical density operator is the one which maximizes the Von-Neumann entropy $$S=-k\cdot\textrm{tr}(\rho\log\rho)$$ under certain constraints. These constraints define different ensembles, e.g.

• Micro canonical ensemble: $$N=\textrm{const} \quad\wedge\quad E=\textrm{const.}$$
• Canonical ensemble: $$N=\textrm{const} \quad\wedge \quad\langle E\rangle=\textrm{const.}$$
• Grand canonical ensemble: $$\langle N \rangle=\textrm{const} \quad\wedge \quad\langle E\rangle=\textrm{const.}$$

From an information theoretic perspective this can be stated as

Axiom: The density operator containing the least information is physical.

as the entropy is a measure for the information contained in the density distribution.

This Occam's razor approach is missing any microscopic/physical argument. Are people working on finding such argument or does it already exist?

• What specifically are you looking for when you refer to a "microscopic/physical argument"? – probably_someone Jun 22 '20 at 22:24
• @probably_someone something which only uses the quantum mechanical axioms. – user224659 Jun 22 '20 at 22:27
• Which axioms are you labeling as "the quantum mechanical axioms"? – probably_someone Jun 22 '20 at 22:27
• @probably_someone The Von-Neumann axioms or some axioms similar to these: cds.cern.ch/record/598319/files/0212126.pdf – user224659 Jun 22 '20 at 22:30