Relating a System's Hamiltonian to Its Entropy Production Using a Complex Time Approach.

Area of Science:

• Theoretical Physics
• Thermodynamics
• Quantum Mechanics

Background:

• Traditional thermodynamics often treats reversible and irreversible processes separately.
• Understanding the interplay between conserved quantities like the Hamiltonian and entropy production is crucial.
• Complex time formalisms offer novel approaches to physical phenomena.

Purpose of the Study:

• To establish an analytical relationship between Hamiltonian and entropy production based on causality.
• To develop a unified framework for describing both reversible and irreversible systems.
• To explore the physical interpretation of complex time in thermodynamic systems.

Main Methods:

• Exploitation of complex time properties to derive analytical relationships.
• Application of Hilbert transform within quantitative geometrical thermodynamics.
• Analysis of specific systems: alpha particle, black hole, and decaying harmonic oscillator.

Main Results:

• An analytical relationship between Hamiltonian and entropy production is derived.
• A unified framework is presented that analytically handles system irreversibility.
• Physical interpretations for 'imaginary time' and 'imaginary energy' are provided.

Conclusions:

• Complex time provides a powerful tool for unifying thermodynamic descriptions.
• The study offers a new perspective on causality and conserved quantities.
• The framework successfully models diverse systems from stable particles to black holes.