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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 1 year, 5 months |
| seen | 2 days ago | |
| stats | profile views | 116 |
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Jan 17 |
revised |
How to “read” the temperature of an abstract system? erased wrong statement |
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Jan 17 |
comment |
How to “read” the temperature of an abstract system? The point is showing that coupling your system to an external bath results in a probability that goes like $e^{-\beta E}$, for some $\beta$. This is te definition of $T$, and is crux of the matter. Until you've shown this you don't know that "T will just take its value" from the bath, because $T$ is not even defined. |
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Jan 17 |
revised |
How to “read” the temperature of an abstract system? book reference |
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Jan 17 |
comment |
How to “read” the temperature of an abstract system? I posted a real, elaborate answer. Hope that gets the job done. |
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Jan 17 |
answered | How to “read” the temperature of an abstract system? |
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Jan 17 |
revised |
Do amorphous metals undergo conchoidal fracture? added 100 characters in body |
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Jan 17 |
comment |
How to “read” the temperature of an abstract system? Systems flow towards probable states, that is - states that have a large number of micro-states. The (log of the) number of micro states is the entropy. So systems "want" to be in (="go to") states with high entropy, but that usually means states with high energy. The trade-off between entropy and energy is exactly the temperature. In evaporating liquid, for example, the vapor state has a higher entropy, but also a higher energy. Therefore, at low $T$ the system is liquid, but when $T$ is high enough the system prefers to be at a higher energetic state (="pay") because its entropy is higher. |
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Jan 16 |
answered | Do amorphous metals undergo conchoidal fracture? |
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Jan 16 |
comment |
How to “read” the temperature of an abstract system? You wrote the answer. This is the definition of $T$. In the Ising model. for example, there is no sense in talking about "average kinetic energy of the spins" or anything of that sort. I'd say that a good way to think about the temperature in this case is "how far above the ground state can I go", which is roughly equivalent to "how much energy can I pay in order to buy some entropy"? |
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Jan 16 |
answered | Hydrostatic equilibrium of a star derivation |
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Jan 12 |
revised |
Do all closed systems, only considering kinematic/mechanical principles, exhibit time reversal symmetry? external magnetic field (thanks to Ron maimon) |
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Jan 12 |
comment |
Do all closed systems, only considering kinematic/mechanical principles, exhibit time reversal symmetry? @Ron Maimon. You are, of course, right about that, but this is a minor point in my answer. I edited it now. |
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Jan 11 |
comment |
Why doesn't phase space contain acceleration/forces? This is wrong - it's only good for an infinitesimal $\delta t$ later (i.e. to first order in $\delta t$). If you want to know the trajectory you need to know the accelerations. But these can be calculated from the position and velocity. |
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Jan 11 |
comment |
Do all closed systems, only considering kinematic/mechanical principles, exhibit time reversal symmetry? Strictly speaking, in classical mechanics the answer is that the dynamics are fully reversible. However, In the real world you are bounded, even theoretically, by the uncertainty principle, not to mention the outrageous impossibleness of reconstructing the the system with reversed velocities. Also, many-body dynamics are generically chaotic, and infinitesimal deviations of initial conditions will result in a significantly different evolution. |
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Jan 11 |
answered | Do all closed systems, only considering kinematic/mechanical principles, exhibit time reversal symmetry? |
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Jan 10 |
answered | Why doesn't phase space contain acceleration/forces? |
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Jan 9 |
awarded | Commentator |
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Jan 9 |
comment |
Calculating Fraunhofer diffraction patterns The homework tag was not there, if I recall correctly, but even if it was, I was not aware of this policy. I will abide in the future... |
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Jan 8 |
answered | Calculating Fraunhofer diffraction patterns |
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Jan 4 |
comment |
Which symmetry is associated with conservation of flux? Could you give a different example? The example you gave is not a conservation law, but merely an integral formulation of the fact that $\nabla^2 \phi=\rho$. Also, when introducing relativistic effects, it is not true anymore. |
