This is the "normal" condition in the macroscopic world, and is always the case for the translational, vibrational, rotational, and non-spin-related electronic and nuclear modes. The relationship suggests that a positive temperature corresponds to the condition where entropy, S, increases as thermal energy, q rev, is added to the system. The definition of thermodynamic temperature T is a function of the change in the system's entropy S under reversible heat transfer Q rev: This spontaneous ordering in equilibrium statistical mechanics goes against common physical intuition that increased energy leads to increased disorder. For example in Onsager's point-vortex analysis negative temperature is associated with the emergence of large-scale clusters of vortices. The limited range of states accessible to a system with negative temperature means that negative temperature is associated with emergent ordering of the system at high energies. Some systems, however (see the examples below), have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease. For a system of ordinary (quantum or classical) particles such as atoms or dust, the number of high energy states is unlimited (particle momenta can in principle be increased indefinitely). This is only possible if the number of high energy states is limited. The possibility of a decrease in entropy as energy increases requires the system to "saturate" in entropy. Thermodynamic systems with unbounded phase space cannot achieve negative temperatures: adding heat always increases their entropy. Systems with a positive temperature will increase in entropy as one adds energy to the system, while systems with a negative temperature will decrease in entropy as one adds energy to the system. The paradox is resolved by considering the more rigorous definition of thermodynamic temperature as the tradeoff between internal energy and entropy contained in the system, with " coldness", the reciprocal of temperature, being the more fundamental quantity. The existence of negative temperature, let alone negative temperature representing "hotter" systems than positive temperature, would seem paradoxical in this interpretation. Temperature is loosely interpreted as the average kinetic energy of the system's particles. A standard example of such a system is population inversion in laser physics. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system. For energies exceeding the value where the peak occurs, the entropy decreases as energy increases, and high-energy states necessarily have negative Boltzmann temperature.Ī system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. As shown by Onsager, a system with bounded phase space necessarily has a peak in the entropy as energy is increased. Bounded phase space is the essential property that allows for negative temperatures, and can occur in both classical and quantum systems. Onsager was investigating 2D vortices confined within a finite area, and realized that since their positions are not independent degrees of freedom from their momenta, the resulting phase space must also be bounded by the finite area. The possibility of negative temperatures was first predicted by Lars Onsager in 1949. However, in particular isolated systems, the temperature defined in terms of Boltzmann's entropy can become negative. Usually, system temperatures are positive. The absolute temperature (Kelvin) scale can be understood loosely as a measure of average kinetic energy. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero. Infinite temperature (coldness zero) is shown at the top of the diagram positive values of coldness/temperature are on the right-hand side, negative values on the left-hand side.Ĭertain systems can achieve negative thermodynamic temperature that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. 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. Please discuss this issue on the article's talk page. Please read the layout guide and lead section guidelines to ensure the section will still be inclusive of all essential details. Please help by moving some material from it into the body of the article. This article's lead section may be too long for the length of the article.
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