Version 1
: Received: 21 February 2023 / Approved: 23 February 2023 / Online: 23 February 2023 (07:40:45 CET)
Version 2
: Received: 24 March 2023 / Approved: 27 March 2023 / Online: 27 March 2023 (07:41:38 CEST)
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach. Entropy2023, 25, 629.
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach. Entropy 2023, 25, 629.
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach. Entropy2023, 25, 629.
Parker, M.C.; Jeynes, C. Relating a System’s Hamiltonian to Its Entropy Production Using a Complex Time Approach. Entropy 2023, 25, 629.
Abstract
We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two conserved quantities of a system’s Hamiltonian and its Entropy Production. In natural units, when complexified, 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 a 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). The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment the complexification of time also enables a meaningful physical interpretation of both “imaginary time” and “imaginary energy”.
Keywords
QGT; entropic Hamiltonian; Bekenstein-Hawking relation; analytical continuation; Wick rotation; Loschmidt Paradox; Riemannian geometry; Kramers-Kronig relations; Arrow of Time
Subject
Physical Sciences, Thermodynamics
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.
Received:
27 March 2023
Commenter:
Chris Jeynes
Commenter's Conflict of Interests:
Author
Comment:
This is the Revised version following peer-review. It is a major Revision with one new section and one section completely rewritten (and many other changes)
Commenter: Chris Jeynes
Commenter's Conflict of Interests: Author