Relating a System’s Hamiltonian to its Entropy Production Using a Complex-Time Approach

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”.

Ab Initio Thermodynamics Calculation of Beta Decay Rates

“…Note also that the "exertion" quantity in QGT is equivalent to the quantity that Edwin Jaynes calls "caliber". [23] Therefore, the quantity Δ can also be interpreted as representing the appropriate entropic sum-over-histories that achieves a particular change in the number of DoFs over the course of a Table 1. Half-lives of various systems, measured (Gonzales et al [28] Audi et al [29] Duer et al [8] ), and calculated by QGT.…”