  In this paper, we show that the time evolution of the Bloch vector governed
by the thermal Jaynes-Cummings model is equivalent to a compressible inviscid
flow with zero vorticity. Because of its quasiperiodicity, the dynamics of the
Bloch vector includes countably infinite angular momenta as integrals of
motion. Moreover, to derive the Bloch vector, we trace out the Hilbert space of
the cavity field and remove entanglement between the single atom and the cavity
mode. These facts indicate that the dynamics of the Bloch vector can be
described with a hidden-variable model that has local determinism and a
countably infinite number of degrees of freedom. Our results fit these
considerations.
