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

Tags:
1. Feb 19, 2017

### Shaun Harlow

I am only aware that the formula has to do with entropy/thermodynamics. I could really use the help on how it applies in physics and what the formula is really about.

2. Feb 20, 2017

### stevendaryl

Staff Emeritus
In that equation, $S$ is the entropy and $E$ is the energy. In thermodynamics, temperature can be defined as:

$\frac{1}{T} = \frac{dS}{dE}$

So your inequality just says $T \gg 0$. So the temperature is well above absolute zero.

3. Feb 20, 2017

### stevendaryl

Staff Emeritus
That definition of temperature assumes that entropy increases with energy (so $T$ is always positive), which is true for classical thermodynamics, but for systems with a discrete number of states, it's possible for $S$ to decrease with $E$, which leads to the bizarre notion of a negative absolute temperature.

4. Feb 20, 2017

### Shaun Harlow

So the inequality is saying that the temperature is above zero? If so, you talk of the "bizarre notion" of a negative absolute temperature that some people infer, but that is not possible correct?

5. Feb 20, 2017

### stevendaryl

Staff Emeritus
The symbol $\gg$ means "much greater than". So the temperature isn't just positive, it's pretty high.

Negative temperatures are not possible in classical thermodynamics, but there are quantum systems where a negative temperature is possible. A negative temperature means that the entropy goes down instead of up when the system gets more energy.

6. Feb 20, 2017

### Shaun Harlow

Alright! Thank you so much you have helped me better understand this and even went deeper into the meaning without making it hard to understand. I really couldn't thank you enough :)