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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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Relating a System's Hamiltonian to Its Entropy Production Using a Complex Time Approach.

Michael C Parker1, Chris Jeynes2

  • 1School of Computer Sciences & Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK.

Entropy (Basel, Switzerland)
|May 16, 2023
PubMed
Summary
This summary is machine-generated.

This study reveals a causal link between a system's Hamiltonian and entropy production using complex time. This framework unifies microscopic and macroscopic scales, handling both reversible and irreversible processes analytically.

Keywords:
Bekenstein–Hawking relationKramers–Kronig relationsLoschmidt ParadoxQGTRiemannian geometryanalytical continuationarrow of timeentropic Hamiltonian

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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.