One Way (? Trapdoor) Permutation of a Bennett's Turing Machine.

Congratulations to Alexandre De Castro upon publication of his paper, One-way-ness in the input-saving (Turing) machine, last month in the journal Physica A.

Alexandro purportedly demonstrates that a thermodynamic information-heat engine running infinitesimally close to boundary conditions is reversible if computed without entropy constraint, but non-invertible with entropy constraint. The implication being that a one way permutation is feasible and therefore, by imputation, P≠NP.
I’m still of the opinion that Alex’s exposition approximates a physical analogue of the function set forth in this blog?
Does an adiabatic thermodynamic bath constitute a ‘trapdoor’?
P.S; Alexandre doesn’t necessarily agree that my function is one way.

*Original Bennett paper here: Logical Reversibility of Computation (1973)