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"Energy has to do with possibilities. Entropy has to do with the probabilities of those possibilities happening. It takes energy and performs a further epistemological step." Constantino Tsallis [1]

Entropy was first described by Rudolf Julius Emanuel Clausius in 1865 [2]. The statistical mechanical desciption is due to Ludwig Eduard Boltzmann (Ref. ?).

Classical thermodynamics[edit]

In classical thermodynamics one has the entropy, S,

{{\mathrm  d}}S={\frac  {\delta Q_{{{\mathrm  {reversible}}}}}{T}}

where Q is the heat and T is the temperature.

Statistical mechanics[edit]

In statistical mechanics entropy is defined by

\left.S\right.:=-k_{B}\sum _{{i=1}}^{W}p_{i}\ln p_{i}

where k_{B} is the Boltzmann constant, i is the index for the microstates, and p_{i} is the probability that microstate i is occupied. In the microcanonical ensemble this gives:

\left.S\right.=k_{B}\ln W

where W (sometimes written as \Omega ) 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

Tsallis entropy[edit]

Tsallis (or non-additive) entropy [3] is defined as (Eq. 1)

S_{q}:=k_{B}{\frac  {1-\sum _{{i=1}}^{W}p_{i}^{q}}{q-1}}

where q is the Tsallis index [4]. As q\rightarrow 1 one recovers the standard expression for entropy. This expression for the entropy is the cornerstone of non-extensive thermodynamics.

Arrow of time[edit]



  • 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:[edit]


  1. http://www.mlahanas.de/Greeks/new/Tsallis.htm
  2. R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie 125 pp. 353-400 (1865)
  3. Constantino Tsallis "Possible generalization of Boltzmann-Gibbs statistics", Journal of Statistical Physics 52 pp. 479-487 (1988)
  4. Filippo Caruso and Constantino Tsallis "Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics", Physical Review E 78 021102 (2008)

Related reading

External links[edit]