Entropy: Difference between revisions

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'''Entropy''' was first described by [[Rudolf Julius Emanuel Clausius]] in 1865 (Ref. 1). The [[statistical mechanics | statistical mechanical]] desciption is due to [[Ludwig Eduard Boltzmann]] (Ref. ?).
==Classical thermodynamics==
==Classical thermodynamics==
In [[classical thermodynamics]] one has the '''entropy''', S,
In [[classical thermodynamics]] one has the '''entropy''', S,
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==References==
==References==
#[http://dx.doi.org/10.1002/andp.18652010702 R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie '''125''' pp. 353-400 (1865)]
#Ya. G. Sinai, "On the Concept of Entropy of a Dynamical System," Doklady Akademii Nauk SSSR '''124''' pp. 768-771 (1959)
#Ya. G. Sinai, "On the Concept of Entropy of a Dynamical System," Doklady Akademii Nauk SSSR '''124''' pp. 768-771 (1959)
#[http://dx.doi.org/10.1063/1.1670348 William G. Hoover "Entropy for Small Classical Crystals", Journal of Chemical Physics '''49''' pp. 1981-1982 (1968)]
#[http://dx.doi.org/10.1063/1.1670348 William G. Hoover "Entropy for Small Classical Crystals", Journal of Chemical Physics '''49''' pp. 1981-1982 (1968)]
[[category:statistical mechanics]]
[[category:statistical mechanics]]
[[Classical thermodynamics]]
[[Classical thermodynamics]]

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Entropy was first described by Rudolf Julius Emanuel Clausius in 1865 (Ref. 1). The statistical mechanical desciption is due to Ludwig Eduard Boltzmann (Ref. ?).

Classical thermodynamics

In classical thermodynamics one has the entropy, S,

where is the heat and is the temperature.

Statistical mechanics

In statistical mechanics the entropy, S, is defined by

where is the Boltzmann constant, m is the index for the microstates, and is the probability that microstate m is occupied. In the microcanonical ensemble this gives:

where (sometimes written as ) is the number of microscopic configurations that result in the observed macroscopic description of the thermodynamic system. This equation provides a link between classical thermodynamics and statistical mechanics

Arrow of time

Articles:

Books:

  • Steven F. Savitt (Ed.) "Time's Arrows Today: Recent Physical and Philosophical Work on the Direction of Time", Cambridge University Press (1997) ISBN 0521599458
  • Michael C. Mackey "Time's Arrow: The Origins of Thermodynamic Behavior" (1992) ISBN 0486432432
  • Huw Price "Time's Arrow and Archimedes' Point New Directions for the Physics of Time" Oxford University Press (1997) ISBN 978-0-19-511798-1

See also:

Interesting reading

References

  1. R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie 125 pp. 353-400 (1865)
  2. Ya. G. Sinai, "On the Concept of Entropy of a Dynamical System," Doklady Akademii Nauk SSSR 124 pp. 768-771 (1959)
  3. William G. Hoover "Entropy for Small Classical Crystals", Journal of Chemical Physics 49 pp. 1981-1982 (1968)

Classical thermodynamics