# Relativistic Boltzmann (including QM) equation from entropy?

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1. Jun 13, 2015

### ohannuks

I'm interested in the derivation of relativistic boltzmann equation from entropy after reading Scott Dodelson's wonderful cosmology book. Does anyone know of any good readings for this?

The usual way of doing things in classical mechanics is to assume $\frac{dN}{dt}= 0$ and go from there; but boltzmann eq. can also be derived starting from maximizing entropy.

I wonder if there is any similar derivation for e.g. quantum field theory or just special/general relativistic theory. The assumption $\frac{dN}{dt}= 0$ is not applicable in the quantum field theory.

2. Jun 13, 2015

### vanhees71

For the classical derivation of the (special-)relativistic Boltzmann equation, see

http://fias.uni-frankfurt.de/~hees/publ/kolkata.pdf

and the references listed therein (particularly I like Cercignani's book).

I've not manage to write up anything like this using non-equilibrium QFT. For a good introduction, see

W. Cassing From Kadanoff-Baym dynamics to off-shell parton transport, Eur. Phys. J. ST 168 (2009) 3-87
http://dx.doi.org/10.1140/epjst/e2009-00959-x
http://arxiv.org/abs/arXiv:0808.0715

3. Jun 14, 2015

### ohannuks

Thank you a lot!