[HN Gopher] Negative Temperature
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       Negative Temperature
        
       Author : dave1010uk
       Score  : 20 points
       Date   : 2024-07-08 20:35 UTC (2 hours ago)
        
 (HTM) web link (en.wikipedia.org)
 (TXT) w3m dump (en.wikipedia.org)
        
       | derbOac wrote:
       | 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.
        
         | Anon84 wrote:
         | 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.
        
       | Anon84 wrote:
       | 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
        
       | skulk wrote:
       | 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.
        
         | Smaug123 wrote:
         | 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...
         | .
        
       | amelius wrote:
       | > 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?
        
         | n3t wrote:
         | Arithmetic underflow, obviously.
        
         | gfxxxx wrote:
         | 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
        
         | jessriedel wrote:
         | 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).
        
         | smegsicle wrote:
         | negative temperature is like a burrito
        
       | mjfl wrote:
       | 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.
        
       | Ygg2 wrote:
       | I always keep remembering Discworld of coming out the far side.
       | 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.
        
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