Dynamical systems and thermodynamics

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SUMMARY

This discussion centers on the mathematical representation of dissipative dynamical systems in relation to thermodynamic laws. The primary focus is on modeling stress as a function of time and strain, utilizing variables such as σ (stress), t (time), ε (strain), and constants kt and kε. Participants seek specific references and detailed methodologies to substantiate the connection between dynamical systems and thermodynamics. The inquiry emphasizes the need for rigorous mathematical frameworks to validate these principles.

PREREQUISITES
  • Understanding of dynamical systems theory
  • Familiarity with thermodynamics principles
  • Knowledge of stress-strain relationships in materials
  • Basic mathematical modeling techniques
NEXT STEPS
  • Research mathematical modeling of dissipative systems
  • Explore the relationship between stress and strain in materials
  • Study the laws of thermodynamics in the context of dynamical systems
  • Investigate relevant literature on mathematical frameworks for thermodynamic validation
USEFUL FOR

Researchers, physicists, and engineers interested in the intersection of dynamical systems and thermodynamics, particularly those focused on material behavior under stress and strain conditions.

JRR
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Is there a mathematical way to show that a dissipative (or general?) dynamical system obeys the laws of thermodynamics?

I am looking for books/sites/references, thanks for any reply.
 
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Thanks for your reply.
The system would typically be the development of stress versus time, or alternatively stress versus strain for a given strain rate.
The simplest form I could think of is this (two variants, as described above):

15zqbg8.png


Where σ is the stress, t is time, ε is strain and kt and kε are constants.
 

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