Kac ring

In statistical mechanics, the Kac ring is a toy model[1] introduced by Mark Kac in 1956[2][3] to explain how the second law of thermodynamics emerges from time-symmetric interactions between molecules (see reversibility paradox). Although artificial,[4] the model is notable as a mathematically transparent example of coarse-graining[5] and is used as a didactic tool[6] in non-equilibrium thermodynamics.

  1. ^ Luczak, Joshua (2017). "Talk about toy models". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 57: 1–7. Bibcode:2017SHPMP..57....1L. doi:10.1016/j.shpsb.2016.11.002. S2CID 125757671.
  2. ^ Kac, Mark (1956). "Some remarks on the use of probability in classical statistical mechanics". Bulletins de l'Académie Royale de Belgique. 42: 356–361.
  3. ^ Thompson, Colin J (1986). "The contributions of Mark Kac to mathematical physics". The Annals of Probability. 14 (4): 1129–1138. doi:10.1214/aop/1176992357.
  4. ^ Kac, Mark (1959). Probability and related topics in physical sciences. American Mathematical Soc.
  5. ^ Gottwald and Oliver (2009). "Boltzmann's Dilemma: An Introduction to Statistical Mechanics via the Kac Ring". SIAM Review. 51 (3): 613–635. Bibcode:2009SIAMR..51..613G. doi:10.1137/070705799.
  6. ^ Dorfman, Jay Robert (1999). An Introduction to Chaos in Nonequilibrium Statistical Mechanics. Cambridge University Press. pp. 34–39.