I always keep remembering Discworld of going one way and becoming the extreme. Rephrased from Moving pictures:
> Not simply, ordinarily cold. Ordinary cold was merely the absence of movement. It has passed through there a long time ago, had gone straight through commonplace idleness and out the far side. It put more effort into staying still than most things put into movement.
Temperature, thermodynamically, is the quantity dQ/dS, which is sort of related to how much the internal energy of the system changes as the system gets bigger, or has more 'stuff' in it, it's like an average energy.
We experience temperature, however, as the amount of heat coming from an object. Really the experience of temperature should then be something like -dS/dQ which is like how readily the system gives up energy. The more entropy increases when the energy in the system decreases, the more 'hot' it feels.
Therefore, our 'experience' of temperature is like -1/T = -dS/dQ. The hottest temperatures are negative numbers close to zero.
Additionally, infinity temperature is simply the crossover point where adding additional heat begins to decrease entropy instead of increasing it. I.e. the places to store the additional heat are running out.
I've read and watched different attempts at explaining negative temperature, and the Wikipedia article is actually the one that has made the most sense to me.
The concept still seems "off" to me intuitively, like an abuse of notation or something, although I understand it logically.
It's usually a consequence of working in the microcanonical ensemble, where you're forcing the energy of the system to be fixed while exploring its various states. The most common (and intuitive) scenario is the Macrocanonical ensemble where the temperature is fixed the energy is allowed to vary. In this case, of course, there is no negative temperature.
> SI temperature/coldness conversion scale: Temperatures on the Kelvin scale are shown in blue (Celsius scale in green, Fahrenheit scale in red), coldness values in gigabyte per nanojoule are shown in black
gigabyte per nanojoule? wat? I understand that this is some measure of entropy but the article never mentions bytes again which is slightly baffling.
Temperature is indeed related to entropy and energy. Entropy is a measure of information, and at a microscopic level is defined similarly in physics and in information theory. (And can be converted from SI units to bits.)
Negative thermodynamic temperatures are "hotter" in the sense that energy will spontaneously flow from a system with negative temperature to a system with positive temperature if those systems are in contact. It's easier to think in terms of the inverse of the temperature ("coldness" or "thermodynamic beta"): energy flows towards higher coldness, and you no longer have any special cases.
Here's an intuition that might help: Suppose we define β=1/T, the reciprocal of temperature. (See https://en.wikipedia.org/wiki/Thermodynamic_beta.) As a system gets hotter and hotter, T gets bigger and bigger, so β falls closer and closer to zero. If β falls past zero and becomes negative, then T will also be negative.
(Also: If T=0, then β would be undefined/infinity. This corresponds to the fact that absolute zero temperature is impossible. β is arguably a more natural way of thinking about temperature than T is.)
How you interpret is that it's pop science misinterpretation. Temperature is necessarily defined for systems in equilibrium. Systems with "negative T" aren't in equilibrium hence T isn't strictly defined.
So, what do we mean by neg T? Solutions to Boltzmann's distribution for population inversion (more electrons, say, in an excited state than the ground state).
Usually, the hotter something is, the more excited states are occupied; but in equilibrium there are always more occupied ground states.
So "hotter than any positive T" refers to "negative T"s having more excited states than positive T
It just means that in a negative-temp system the number of states with a given energy gets smaller as energy goes up rather than, as for the vast majority of systems (which have positive temperature), getting larger. That means that energy will flow even more quickly to the positive-temp system from the negative-temp system than it would from any positive-temp system, because each unit of energy transfered enlarges the state space of both systems (rather than enlarging one and shrinking the other so as to simply produce a net increase in the number of states, as is the case for most spontaneous energy flows).
Cool. I actually worked on this back in the early days of my PhD (https://arxiv.org/pdf/0705.2385). Never expected to see it on HN
I always keep remembering Discworld of going one way and becoming the extreme. Rephrased from Moving pictures:
Temperature, thermodynamically, is the quantity dQ/dS, which is sort of related to how much the internal energy of the system changes as the system gets bigger, or has more 'stuff' in it, it's like an average energy.
We experience temperature, however, as the amount of heat coming from an object. Really the experience of temperature should then be something like -dS/dQ which is like how readily the system gives up energy. The more entropy increases when the energy in the system decreases, the more 'hot' it feels.
Therefore, our 'experience' of temperature is like -1/T = -dS/dQ. The hottest temperatures are negative numbers close to zero.
Additionally, infinity temperature is simply the crossover point where adding additional heat begins to decrease entropy instead of increasing it. I.e. the places to store the additional heat are running out.
I've read and watched different attempts at explaining negative temperature, and the Wikipedia article is actually the one that has made the most sense to me.
The concept still seems "off" to me intuitively, like an abuse of notation or something, although I understand it logically.
It's usually a consequence of working in the microcanonical ensemble, where you're forcing the energy of the system to be fixed while exploring its various states. The most common (and intuitive) scenario is the Macrocanonical ensemble where the temperature is fixed the energy is allowed to vary. In this case, of course, there is no negative temperature.
From the main image caption:
> SI temperature/coldness conversion scale: Temperatures on the Kelvin scale are shown in blue (Celsius scale in green, Fahrenheit scale in red), coldness values in gigabyte per nanojoule are shown in black
gigabyte per nanojoule? wat? I understand that this is some measure of entropy but the article never mentions bytes again which is slightly baffling.
Temperature is indeed related to entropy and energy. Entropy is a measure of information, and at a microscopic level is defined similarly in physics and in information theory. (And can be converted from SI units to bits.)
I am certainly no expert and couldn't have even begun to put an order of magnitude estimate on any of the quantities involved, but it sounded plausible. Source appears to be https://arxiv.org/abs/cond-mat/9711074 per https://en.wikipedia.org/wiki/Thermodynamic_beta#cite_note-c... .
> A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature.
How to interpret this sentence?
Negative thermodynamic temperatures are "hotter" in the sense that energy will spontaneously flow from a system with negative temperature to a system with positive temperature if those systems are in contact. It's easier to think in terms of the inverse of the temperature ("coldness" or "thermodynamic beta"): energy flows towards higher coldness, and you no longer have any special cases.
Here's an intuition that might help: Suppose we define β=1/T, the reciprocal of temperature. (See https://en.wikipedia.org/wiki/Thermodynamic_beta.) As a system gets hotter and hotter, T gets bigger and bigger, so β falls closer and closer to zero. If β falls past zero and becomes negative, then T will also be negative.
(Also: If T=0, then β would be undefined/infinity. This corresponds to the fact that absolute zero temperature is impossible. β is arguably a more natural way of thinking about temperature than T is.)
Arithmetic underflow is not a bad explanation.
How you interpret is that it's pop science misinterpretation. Temperature is necessarily defined for systems in equilibrium. Systems with "negative T" aren't in equilibrium hence T isn't strictly defined.
So, what do we mean by neg T? Solutions to Boltzmann's distribution for population inversion (more electrons, say, in an excited state than the ground state).
Usually, the hotter something is, the more excited states are occupied; but in equilibrium there are always more occupied ground states.
So "hotter than any positive T" refers to "negative T"s having more excited states than positive T
It just means that in a negative-temp system the number of states with a given energy gets smaller as energy goes up rather than, as for the vast majority of systems (which have positive temperature), getting larger. That means that energy will flow even more quickly to the positive-temp system from the negative-temp system than it would from any positive-temp system, because each unit of energy transfered enlarges the state space of both systems (rather than enlarging one and shrinking the other so as to simply produce a net increase in the number of states, as is the case for most spontaneous energy flows).
Arithmetic underflow, obviously.
negative temperature is like a burrito