Negative temperature

In physics, certain systems can achieve negative temperatures; that is, their thermodynamic temperature can be a negative quantity. Negative temperatures can be expressed as negative numbers on the kelvin scale.
Temperatures that are expressed as negative numbers on the familiar Celsius or Fahrenheit scales are simply colder than the zero points of those scales. By contrast, a system with a truly negative temperature is not colder than absolute zero; in fact, temperatures colder than absolute zero are impossible by definition. Rather, a system with a truly negative Kelvin temperature is hotter than any system with a positive temperature (in the sense that if a negativetemperature system and a positivetemperature system come in contact, heat will flow from the negative to the positivetemperature system).
Most familiar systems cannot achieve negative temperatures, because adding energy always increases their entropy. 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. Because temperature may be formally defined by the relationship between energy and entropy, such a system's temperature becomes negative, even though energy is being added  implying that the system's heat capacity is negative.
Contents
Heat and molecular energy distribution
Negative temperatures can only exist in a system where there are a limited number of energy states (see below). As the temperature is increased on such a system, particles move into higher and higher energy states, and as the temperature increases, the number of particles in the lower energy states and in the higher energy states approaches equality. (This is a consequence of the definition of temperature in statistical mechanics for systems with limited states.) By injecting energy into these systems in the right fashion, it is possible to create a system in which there are more particles in the higher energy states than in the lower ones. The system can then be characterised as having a negative temperature. A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature. As Kittel and Kroemer (p. 462) put it, "The temperature scale from cold to hot runs:
 +0 K, . . . , +300 K, . . . , +∞ K, −∞ K, . . . , −300 K, . . . , −0 K."
Generally, temperature as it is felt is defined by the kinetic energy of atoms. Since there is no upper bound on momentum of an atom there is no upper bound to the number of energy states available if enough energy is added, and no way to get to a negative temperature. However, temperature is more generally defined by statistical mechanics than just kinetic energy (see below). The inverse temperature β = 1/kT (where k is Boltzmann's constant) scale runs continuously from low energy to high as +∞, . . . , −∞.
Temperature and disorder
The distribution of energy among the various translational, vibrational, rotational, electronic, and nuclear modes of a system determines the macroscopic temperature. In a "normal" system, thermal energy is constantly being exchanged between the various modes.
However, for some cases it is possible to isolate one or more of the modes. In practice the isolated modes still exchange energy with the other modes, but the time scale of this exchange is much slower than for the exchanges within the isolated mode. One example is the case of nuclear spins in a strong external magnetic field. In this case, energy flows fairly rapidly among the spin states of interacting atoms, but energy transfer between the nuclear spins and other modes is relatively slow. Since the energy flow is predominantly within the spin system, it makes sense to think of a spin temperature that is distinct from the temperature due to other modes.
A definition of temperature can be based on the relationship:
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. This is the "normal" condition in the macroscopic world, and is always the case for the translational, vibrational, rotational, and nonspin related electronic and nuclear modes. The reason for this is that there are an infinite number of these types of modes, and adding more heat to the system increases the number of modes that are energetically accessible, and thus increases the entropy.
Examples
Nuclear spins
In the case of electronic and nuclear spin systems there are only a finite number of modes available, often just two, corresponding to spin up and spin down. In the absence of a magnetic field, these spin states are degenerate, meaning that they correspond to the same energy. When an external magnetic field is applied, the energy levels are split, since those spin states that are aligned with the magnetic field will have a different energy from those that are antiparallel to it.
In the absence of a magnetic field, such a twospin system would have maximum entropy when half the atoms are in the spinup state and half are in the spindown state, and so one would expect to find the system with close to an equal distribution of spins. Upon application of a magnetic field, some of the atoms will tend to align so as to minimize the energy of the system, thus slightly more atoms should be in the lowerenergy state (for the purposes of this example we'll assume the spindown state is the lowerenergy state). It is possible to add energy to the spin system using radio frequency (RF) techniques (Spectroscopy with coherent radiation: selected papers of Norman F. Ramsey with commentary. World Scientific Series in 20th Century Physics Vol. 21, 1998. Page xxxi, (h)). This causes atoms to flip from spindown to spinup.
Since we started with over half the atoms in the spindown state, initially this drives the system towards a 50/50 mixture, so the entropy is increasing, corresponding to a positive temperature. However, at some point more than half of the spins are in the spinup position. In this case, adding additional energy reduces the entropy, since it moves the system further from a 50/50 mixture. This reduction in entropy with the addition of energy corresponds to a negative temperature.
Lasers
This phenomenon can also be observed in many lasing systems, wherein a large fraction of the system's atoms (for chemical and gas lasers) or electrons (in semiconductor lasers) are in excited states. This is referred to as a population inversion.
The Hamiltonian for a single mode of a luminescent radiation field at frequency ν is
The density operator in the grand canonical ensemble is
For the system to have a ground state, the trace to converge, and the density operator to be generally meaningful, βH must be positive semidefinite. So if hν < μ, and H is negative semidefinite, then β must itself be negative, implying a negative temperature.
See also
References
 Kittel, Charles; Herbert Kroemer (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0716710889.
 Castle, Jack Jr.; Werner Emmerich; Robert Heikes; Robert Miller; John Rayne (1965). Science by degrees: Temperature from Zero to Zero. a Westinghouse Search Book by Walker and Company, New York.
 Montgomery, David C. (19720410). "Twodimensional vortex motion and "negative temperatures"". Physics Letters A 39 (1): 7–8. Bibcode 1972PhLA...39....7M. doi:10.1016/03759601(72)903027.
 Edwards, Samuel F.; J. Bryan Taylor (19740205). "Negative Temperature States of TwoDimensional Plasmas and Vortex Fluids". Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 336 (1606): 257–271. Bibcode 1974RSPSA.336..257E. doi:10.1098/rspa.1974.0018. JSTOR 78450.
 Hsu, Wenyue; Richard Barakat (19920915). "Statistics and thermodynamics of luminescent radiation". Physical Review B 46 (11): 6760–6767. Bibcode 1992PhRvB..46.6760H. doi:10.1103/PhysRevB.46.6760. http://link.aps.org/abstract/PRB/v46/p6760.
Further reading
 Purcell, Edward M.; Robert V. Pound (19510115). "A Nuclear Spin System at Negative Temperature". Physical Review 81 (2): 279–280. Bibcode 1951PhRv...81..279P. doi:10.1103/PhysRev.81.279. http://link.aps.org/abstract/PR/v81/p279.
 Ramsey, Norman F. (19560701). "Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures". Physical Review 103 (1): 20–28. Bibcode 1956PhRv..103...20R. doi:10.1103/PhysRev.103.20. http://link.aps.org/abstract/PR/v103/p20.
 Sitek, Ted (2005). "ENTROPY–a root cause of Aging and the Widespread Fatigue Damage". Federal Aviation Administration USA. http://dmses.dot.gov/docimages/pdf96/399807_web.pdf.
 Tremblay, AndréMarie (19751118). "Comment on: Negative Kelvin temperatures: some anomalies and a speculation". American Journal of Physics 44 (10): 994–995. Bibcode 1976AmJPh..44..994T. doi:10.1119/1.10248. http://www.physique.usherbrooke.ca/~tremblay/articles/Comment%20on%20%27Negative%20Kelvin%20temperatures,%20Some%20anomalies%20and%20a%20speculation%27.%20Tremblay.pdf.
External links
 Recent applications
 Parihar; Widom; Srivastava (2006). "Thermal Time Scales in a Color Glass Condensate". Physical Review C 73 (17901). arXiv:hepph/0505199. Bibcode 2006PhRvC..73a7901P. doi:10.1103/PhysRevC.73.017901.
 Mosk (2005). "Atomic Gases at Negative Kinetic Temperature". Physical Review Letters 95 (4). arXiv:condmat/0501344. Bibcode 2005PhRvL..95d0403M. doi:10.1103/PhysRevLett.95.040403.
 Harry Schmidt; Guenter Mahler (2005). "Control of Local Relaxation Behavior in Closed Bipartite Quantum Systems". Physical Review E 72 (7). arXiv:quantph/0502181. Bibcode 2005PhRvE..72a6117S. doi:10.1103/PhysRevE.72.016117.
 GonzalezDiaz (2004). "Dark energy and supermassive black holes". Physical Review D 70 (6). arXiv:astroph/0408450. Bibcode 2004PhRvD..70f3530G. doi:10.1103/PhysRevD.70.063530.
 Jian Qi Shen (2003). "Antishielding Effect and Negative Temperature in Instantaneously Reversed Electric Fields and LeftHanded Media". Physica Scripta 68: 87–97. arXiv:condmat/0302351. Bibcode 2003PhyS...68...87S. doi:10.1238/Physica.Regular.068a00087.
 Varga, Peter (1998). "Minimax games, spin glasses, and the polynomialtime hierarchy of complexity classes". Physical Review E 57 (6): 6487–6492. arXiv:abs/condmat/9604030. Bibcode 1998PhRvE..57.6487V. doi:10.1103/PhysRevE.57.6487.
Categories: Temperature
 Magnetism
 Laser science
 Plasma physics
Wikimedia Foundation. 2010.
Look at other dictionaries:
negative temperature — neigiamoji temperatūra statusas T sritis fizika atitikmenys: angl. negative temperature vok. negative Temperatur, f rus. отрицательная температура, f pranc. température négative, f … Fizikos terminų žodynas
negative temperature — neigiamoji temperatūra statusas T sritis Standartizacija ir metrologija apibrėžtis Temperatūra, žemesnė už 0 ºC. atitikmenys: angl. negative temperature vok. negative Temperatur, f rus. отрицательная температура, f pranc. température au dessous… … Penkiakalbis aiškinamasis metrologijos terminų žodynas
Negative temperature coefficient — A negative temperature coefficient (NTC) occurs when the thermal conductivity of a material rises with increasing temperature, typically in a defined temperature range. For most materials, the thermal conductivity will decrease with increasing… … Wikipedia
negative temperature coefficient resistor — neigiamojo temperatūrinio varžos koeficiento varžas statusas T sritis radioelektronika atitikmenys: angl. negative temperature coefficient resistor vok. Widerstand mit negativem Widerstandstemperaturkoeffizienten, m rus. резистор с отрицательным… … Radioelektronikos terminų žodynas
negative temperature coefficient of resistance — neigiamasis temperatūrinis varžos koeficientas statusas T sritis radioelektronika atitikmenys: angl. negative temperature coefficient of resistance vok. negativer Widerstandstemperaturkoeffizient, m rus. отрицательный температурный коэффициент… … Radioelektronikos terminų žodynas
negative temperature coefficient — (NTC) a special type of thermistor whose resistance decreases as the temperature increases. Nearly all coolant temperature sensors are NTC thermistors … Dictionary of automotive terms
negative temperature coefficient thermistor — (NTC) Electronic thermistor which decreases in resistance as temperature increases … Dictionary of automotive terms
Temperature measurement — using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Røemer. Fahrenheit … Wikipedia
Temperature — This article is about the thermodynamic property. For other uses, see Temperature (disambiguation). A map of global long term monthly average surface air temperatures i … Wikipedia
Temperature coefficient — The temperature coefficient is the relative change of a physical property when the temperature is changed by 1 K. In the following formula, let R be the physical property to be measured and T be the temperature at which the property is… … Wikipedia