# Is the reciprocal of Entropy easier to understand? [closed]

"A thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system."

The problem with this is that the human mind is bad with negatives.

"unavailability", "disorder".

The universe is running DOWN which means Entropy is going UP.

Is there are word for the reciprocal of entropy?

Would it have been better to have used this concept originally, just as pi would have been better as circ./radius?

• IMHO entropy is best thought of in terms of energy-density, and sameness. If the energy density is the same everywhere there's no available energy, so you can't do any work. However I struggle to come up with a word with the opposite meaning. Difference-ness doesn't quite cut it. – John Duffield Jul 22 '16 at 15:24
• Interpreting entropy as disorder is dangerous, since there are cases where a liquid (the unordered phase) has lower entropy than the corresponding crystal (the ordered phase). Such systems crystalize when the temperature is increased! – David Zwicker Jul 22 '16 at 16:56
• I think this is what you're looking for en.wikipedia.org/wiki/Negentropy – Joshua Meyers Jul 22 '16 at 18:19

Among the important and useful properties of entropy as it is currently defined, entropy is extensive. If I have two systems $A$ and $B$ with entropies $S_A$ and $S_B$, the total entropy of the combined system is $S_\text{total} = S_A + S_B$.

Were you to define "orderedness" as $\eta = 1/S$, that quantity would be neither extensive nor intensive.

The definition of entropy from statistical mechanics, $\exp \frac Sk =\Omega$ where $\Omega$ is the number of indistinguishable states available to your system, is also much more straightforward than the corresponding definition for $\eta$.

If you continue to study thermodynamics, you'll eventually discover that inverse temperature, $1/T$, is better-behaved algebraically than temperature. But we're stuck with that one, too.

• Interesting argument. So when discussing a series electric circuit resistance is extensive, but when discussing parallel electric circuit conductance is extensive instead? And when one is discussing a complicated electric circuit of both series and parallel components one goes back and forth with first resistance and then conductance* and then resistance again being extensive? Perhaps a subtlety is missing from your argument. – Pieter Geerkens Jul 22 '16 at 21:57
• @PieterGeerkens I was actually thinking that $\partial S/\partial U = 1/T$, while $\partial \eta/\partial U =$ a pain in the tail. I left it out because I guessed the OP doesn't have a strong statmech background. – rob Jul 23 '16 at 0:27

The reason we say entropy is a measure of disorder is because of Boltzman's famous statement: $S = k_B \ln\Omega$ where $\Omega$ is the number of different microstates of the system. Ignore the pop culture ideas of entropy (being an artifact of nature) as evil. It simply "is". It is not evil or good. In fact, it is also used as the measure of the amount of information in a system (in information theory). The more you think about pop culture references (and insert their metaphysical beliefs into your study) the less you will be on the true path to scientific knowledge.

Disregard popculture and move on. Also $1/S$ is not useful in anyway, since we can add Entropies together in thermodynamics and in the study of chemical reactions.