  The level statistics in the transition between delocalized and localized
{phases of} many body interacting systems is {considered}. We recall the joint
probability distribution for eigenvalues resulting from the statistical
mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The
resulting single parameter analytic distribution is probed numerically {via
Monte Carlo method}. The resulting higher order spacing ratios are compared
with data coming from different {quantum many body systems}. It is found that
this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian
ensemble -- a single parameter model of level statistics proposed recently in
the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa
distribution is also} only slightly inferior to the two-parameter $\beta$-h
ansatz shown {earlier} to reproduce {level statistics of} physical systems
remarkably well.

Disordered Systems and Neural Networks;Quantum Physics