Thermodynamics : https://www.youtube.com/watch?v=uc9P5yb3Xtc

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SUMMARY

This discussion centers on the relationship between energy and information as presented in the video on thermodynamics. It highlights that while energy remains constant in the universe, entropy increases, leading to a decrease in information. The formula for entropy, given by S=k_B ln(Ω), illustrates how the number of microstates (Ω) correlates with the macrostate of a system. The conversation confirms that even with conservation of energy, the increase in entropy from subsystem interactions results in a greater number of microstates.

PREREQUISITES
  • Understanding of thermodynamic principles
  • Familiarity with the concept of entropy
  • Knowledge of Boltzmann's entropy formula
  • Basic grasp of microcanonical ensembles
NEXT STEPS
  • Explore the implications of the second law of thermodynamics
  • Study the relationship between entropy and information theory
  • Investigate quantum fluctuations and their effects on energy conservation
  • Learn about microcanonical ensembles in statistical mechanics
USEFUL FOR

Students of physics, researchers in thermodynamics, and anyone interested in the interplay between energy, entropy, and information theory will find this discussion beneficial.

TheAnt
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Hi I had a question about this video. Indeed if I understand the video correctly it states that energy is linked to information. But how does that work indeed knowing that energy is constant, that more entropy = less information and that entropy increases. It seems that the universe will end with less information but the same amount of energy.
Thank you.
 
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Entropy can be given by
$$
S=k_B \ln\Omega
$$
where ##\Omega## is the number of microstates that correspond to your known macrostate, and ##k_B## is the Boltzmann constant. This formula holds for a microcanonical ensemble, which means that states close to the energy of the system have prety much the same probability. If you try to combine two such systems, so that they interact, you will see an increase in entropy, which means there are more microstates with the total energy.

So yes by conservation of energy the total energy of the universe will not change (ignoring quantum fluctuations), even though entropy increases due to interactions of subsystems.
 

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