In
statistical mechanics, the
thermodynamic beta (or occasionally
perk) is the reciprocal of the
thermodynamic temperature of a system. Also referred to as coldness, it can be calculated in the
microcanonical ensemble from the formula
where
kB 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
kB=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
ß describes the amount by which the system will "perk up," i.e. randomize. Though completely equivalent in conceptual content to temperature,
ß is generally considered a more fundamental quantity than temperature owing to the phenomenon of
negative temperature, in which
ß is continuous as it crosses zero whereas
T has a singularity.
