The discussion revolves around the formula \( \frac{1}{(dS/dE)} \gg 0 \) and its implications in the context of thermodynamics and entropy. Participants explore the relationship between entropy (S), energy (E), and temperature (T), particularly focusing on the conditions under which temperature is defined and the concept of negative absolute temperatures.
Participants generally agree on the basic relationship between entropy, energy, and temperature, but there is disagreement regarding the existence and implications of negative absolute temperatures, particularly in classical versus quantum contexts.
The discussion highlights the limitations of classical thermodynamics in explaining systems with discrete states and the conditions under which negative temperatures might be considered. There are unresolved aspects regarding the implications of these concepts in different physical contexts.
Shaun Harlow said: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 said: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.
Shaun Harlow said: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 said: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.
stevendaryl said: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.