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

[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.

 

[stevendaryl]

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.

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.

 

[stevendaryl]

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.

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.

 

[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?

 

[stevendaryl]

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?

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.

 

[Shaun Harlow]

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.

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.

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 :)