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thermodynamic beta
In statistical mechanics, the thermodynamic beta (or occasionally perk) is the reciprocal of the thermodynamic temperature of a system.〔J. Castle, W. Emmenish, R. Henkes, R. Miller, and J. Rayne (1965) ''Science by Degrees: Temperature from Zero to Zero'' (Westinghouse Search Book Series, Walker and Company, New York) (snippets ).〕 Also referred to as coldness,〔Claude Garrod (1995) ''Stat Mech and Thermodynamics'' (Oxford U. Press).〕 it can be calculated in the microcanonical ensemble from the formula
:
where ''k''B is the Boltzmann constant, ''S'' is the entropy, ''E'' is the energy, ''V'' is the volume, ''N'' is the particle number, and ''T'' is the absolute temperature. It has units reciprocal to that of energy; in units where ''k''B=1 it also has units reciprocal to that of temperature. Thermodynamic beta is essentially the connection between the information theoretic/statistical interpretation of a physical system through its entropy and the thermodynamics associated with its energy. It express 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 by which the system will "perk up," i.e. randomize. 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.
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