Geodesic
Ultra-Second Quantization and ``Ghosts'' in Quantized Entropy
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 3, pp. 464-490

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We previously constructed the theory of quantum thermodynamics, which assigns operators to dual variables (for example, pressure and volume or temperature and entropy, i.e., dual pairs of extensive and intensive variables similar to momenta and coordinates in classical mechanics) similarly to the theory of quantum mechanics. Here we show that in both the bosonic and fermionic cases, the quantized entropy introduced as an operator in special Fock spaces containing a new variable, called the statistical spin, depends on some variables that do not affect any physical results and are hence called “ghosts”. 
@article{TMF_2001_129_3_a6,
     author = {V. P. Maslov},
     title = {Ultra-Second {Quantization} and {``Ghosts''} in {Quantized} {Entropy}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {464--490},
     publisher = {mathdoc},
     volume = {129},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_129_3_a6/}
}
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V. P. Maslov. Ultra-Second Quantization and ``Ghosts'' in Quantized Entropy. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 3, pp. 464-490. http://geodesic.mathdoc.fr/item/TMF_2001_129_3_a6/