Entropy

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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. ?). The word entropy originated from the Greek word meaning a turning or transformation "τροπή" [3].

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 [4] 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 [5]. 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]

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:[edit]

References[edit]

Related reading

External links[edit]