Laser entropy: from lasers and masers to Bose condensates and black holes

The entropy of an ordinary (photon) laser and an atom laser (Bose condensate) is calculated. In particular, the nonzero entropy of a single mode laser or maser operating near threshold is obtained. This result is to be compared with incorrect arguments frequently made in the study of the maser heat engine to the effect that at threshold maser radiation is characterized by an infinite temperature and its entropy is zero. Similarly, the entropy of the ground state of a Bose-Einstein condensate (a.k.a. the atom laser) is also calculated for the first time. This is to be compared with the textbook wisdom which holds that: 'The condensed particles ... are condensed in momentum space, a set of stationary particles ... having zero energy and zero entropy.' On the other hand, the BEC total entropy is found to be equal to that of the excited state entropy. This is true because the correlation entropy between the ground state and the excited states is equal and opposite to the ground state entropy. Furthermore, we find that the entropy of the radiation emitted by atoms falling into a black hole (BH) can be easily calculated by a laser type quantum master equation. The entropy thus calculated has much in common with Bekenstein-Hawking BH entropy.