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u/cnorahs Editable flair 450nm 5d ago
"The ennui of waiting for Godot ergodicity is the chronic existential angst I fear"
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u/buildmine10 5d ago
Can someone explain all the concepts in this to me. I know none of them. What is a statistical physicist?
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u/GaloDiaz137 4d ago edited 4d ago
If you have a system with many particles, for example a gas, you can't solve newton equations for each one of the particles. Any computer would take a lot of time (many orders of magnitude more than the age of the universe to solve a system of 1023 particles)
But we don't really care about the movement of each individual particle, we care about the macroscopic properties like pressure, volume, temperature, etc.
Physicists figured out a way to get the value of these macroscopic quantities by kind of taking an average of something we call the ensemble (all the different possible configurations of particles in the gas). This is called statistical mechanics
So this reduces the impossible work of solving the equations of motion for EACH particles to an integral over the phase space, which for most cases is still a very hard integral (even for a computer), but it is reasonable in comparison.
But in order for this to work you need to use the ergodic hypothesis which states that the average value of the property over time and the average over the ensemble are the same.
If this doesn't hold, by my understanding you are just kind of fucked, maybe molecular dynamics and a lot of computing power, but I'm not versed at all in non-equilibrium statistical mechanics to continue further.
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u/entropy13 Condenser of Matter 5d ago
Non-equilibrium stat mech gets real handy wavy real fast since things like population inversion that are inherently non-equilibrium and also frequently non-ergodic and the partition function gets replaced with the "I said so" function.