So, I'm hesitant to post this because I get a somewhat crack potty feeling to the book (however, he actually does reference some of your papers in the more "normal" section [i.e section 1.5.2 he references
https://arxiv.org/abs/quant-ph/0305131]), but I'm not sure if that's because my Bohmian mechanics principles are weak (I only know the basic of how they apply the Hamilton-Jacobi equations), but with that being said...
I stumbled upon this book
https://www.amazon.com/dp/9813227974/?tag=pfamazon01-20 in my search for a book to learn this theory.
At the start of chapter 2, he states:
"##S_Q=-\frac{1}{2} \ln \rho##
where ##\rho## is the probability density (describing the space-temporal distribution of an ensemble of particles, namely the density of particles in the element of volume ##d^3 x## around a point ##\vec{x}## at time ##t## )associated with the wave function ##\psi(\vec{x}, t)## of an individual physical system. In the entropic version of Bohmian quantum mechanics, the space-temporal distribution of the ensemble of particles describing the individual physical system under consideration is assumed to generate a modification, a sort of deformation of the background space characterized by the quantity given by equation (2.1). On the basis of equation (2.1), it is plausible to make a parallelism with the standard definition of entropy given by the Boltzmann law, in other words equation (2.1) may be considered indeed as the quantum counterpart of a Boltzmann-type law. In the light of its relation with the wave function, the quantity given by equation (2.1) can be appropriately defined as "quantum entropy". The quantum entropy (2.1) can be interpreted as the physical parameter that, in the quantum domain, measures the degree of order and chaos of the vacuum - a storage of virtual trajectories supplying optimal ones for particle movement - which supports the density ##\rho## describing the space-temporal distribution of the ensemble of particles associated with the wave function under consideration."
So, the issues I have is that everything he references in this part is... his own articles, which IMO isn't THAT big of an issue, it just gets more suspicious because I can't find the journals/papers. But, I'll post this for you, and let you be the judge.
[BTW, in case anyone is interested, I ended up going with
https://www.amazon.com/dp/0521485436/?tag=pfamazon01-20 but just need to actual take time and study the chapters in depth, but it is a nicely written book so far IMO.]