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Concept
Thermodynamic beta
Summary
In statistical thermodynamics, thermodynamic beta, also known as coldness, is the reciprocal of the thermodynamic temperature of a system: (where T is the temperature and kB is Boltzmann constant).
It was originally introduced in 1971 (as Kältefunktion "coldness function") by de, one of the proponents of the rational thermodynamics school of thought, based on earlier proposals for a "reciprocal temperature" function.
Thermodynamic beta has units reciprocal to that of energy (in SI units, reciprocal joules, ). In non-thermal units, it can also be measured in byte per joule, or more conveniently, gigabyte per nanojoule; 1 K−1 is equivalent to about 13,062 gigabytes per nanojoule; at room temperature: T = 300K, β ≈ 44GB/nJ ≈ 39eV−1 ≈ 2.4e20J−1. The conversion factor is 1 GB/nJ = J−1.
Thermodynamic beta is essentially the connection between the information theory and statistical mechanics interpretation of a physical system through its entropy and the thermodynamics associated with its energy. It expresses the response of entropy to an increase in energy. If a system is challenged with a small amount of energy, then β describes the amount the system will randomize.
Via the statistical definition of temperature as a function of entropy, the coldness function can be calculated in the microcanonical ensemble from the formula
(i.e., the partial derivative of the entropy S with respect to the energy E at constant volume V and particle number N).
Though completely equivalent in conceptual content to temperature, β is generally considered a more fundamental quantity than temperature owing to the phenomenon of negative temperature, in which β is continuous as it crosses zero whereas T has a singularity.
In addition, β has the advantage of being easier to understand causally: If a small amount of heat is added to a system, β is the increase in entropy divided by the increase in heat. Temperature is difficult to interpret in the same sense, as it is not possible to "Add entropy" to a system except indirectly, by modifying other quantities such as temperature, volume, or number of particles.
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