One-parameter Darboux transformations in Thermodynamics

Details One-parameter Darboux transformations in Thermodynamics One-parameter Darboux transformations in Thermodynamics

2002-08-08

arxiv.org/abs/math-ph/0208013v1

AIP Conf. Proc. 643 (2002) 471-475

Physics

Mathematical Physics

6 pages, contribution at the AIP 1st International Conference on Quantum Limits to the Second Law, San Diego, CA, (main organi

Scientific paper

10.1063/1.1523847

The quantum oscillator thermodynamic actions are the conjugate intensive parameters for the frequency in any frequency changing process. These oscillator actions fulfill simple Riccati equations. Interesting Darboux transformations of the fundamental Planck and pure vacuum actions are discussed here in some detail. It is shown that the one-parameter "Darboux-Transformed-Thermodynamics" refers to superpositions of boson and fermion excitations of positive and negative absolute temperature, respectively. A Darboux generalization of the fluctuation-dissipation theorem is also briefly sketched

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