Version 1
: Received: 21 February 2023 / Approved: 23 February 2023 / Online: 23 February 2023 (07:40:45 CET)
How to cite:
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to its Entropy Production Using a Complex-Time Approach. Preprints2023, 2023020402. https://doi.org/10.20944/preprints202302.0402.v1.
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to its Entropy Production Using a Complex-Time Approach. Preprints 2023, 2023020402. https://doi.org/10.20944/preprints202302.0402.v1.
Cite as:
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to its Entropy Production Using a Complex-Time Approach. Preprints2023, 2023020402. https://doi.org/10.20944/preprints202302.0402.v1.
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to its Entropy Production Using a Complex-Time Approach. Preprints 2023, 2023020402. https://doi.org/10.20944/preprints202302.0402.v1.
Abstract
We exploit the properties of complex time to obtain an analytical relationship between the two conserved quantities of the (complexified) Entropy Production and the (complexified) system Hamiltonian. In natural units, the one is simply the Wick-rotated complex-conjugate of the other. A Hilbert transform relation is constructed in the formalism of Quantitative Geometrical Thermodynamics which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular the thermodynamics of two unitary entities are considered: the alpha particle which is absolutely stable (that is, trivially reversible with zero entropy production), and the black hole whose absolute disequilibrium (unconditional irreversibility) is characterized by a non-zero entropy production for which we show an alternate derivation confirming our previous one (Universe 7, 2021, 325). In this treatment the complexification of time also enables a meaningful physical interpretation of both “imaginary time” and “imaginary energy”.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
