# I What is the formula 1/(dS/dE)>>0 and how does it apply?

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1. Feb 19, 2017

### Shaun Harlow

I know that it relates to thermodynamics and possibly entropy? It would be greatly appreciated if someone could explain what the formula is about and how it applies to physics.

2. Dec 5, 2017

### Smile Say Hello

This looks more like a criterion (or criteria if you wish). Note that you can rewrite the left hand side as dE/dS. It looks familiar but I cannot put my finger on it. It is essentially saying "when the rate of change of E with respect to S is much greater than 0".

3. Dec 9, 2017

### Mapes

$1/(\partial S/\partial E)$ with entropy $S$ and energy $E$ is the definition of temperature (I've replaced the absolute derivative $d/dx$ with the partial derivative $\partial/\partial x$ because the entropy is a function of several variables; here, we're assuming constant volume $V$ and particle number $N_i$). So the condition implies a relatively high temperature, i.e., a high-temperature limit.