## Tsallis EntropyOctober 29, 2014 Thermodynamics has developed from contributions from scientists of many nationalities. As just a few examples, we have Sadi Carno (1796-1832) from France; Robert Boyle (1627-1691) and William Thomson, Lord Kelvin (1824-1907) from Ireland; James Prescott Joule (1818-1889) from England; Rudolf Clausius (1822-1888) from Germany; James Clerk Maxwell (1831-1879) from Scotland; Josiah Willard Gibbs (1839-1903) from the United States; and Ludwig Boltzmann (1844-1906) from Austria).
S is the entropy, K is the Boltzmann constant (1.38062 x 10_{B}^{-23} joule/kelvin), and Ω is the number of states accessible to the system. This equation is actually a simplification of the Boltzmann-Gibbs entropy when every state has the same probability p; viz,
_{i}S, given by the following equation:
_{q}q, is called the entropic-index. This equation becomes the Boltzmann-Gibbs entropy equation when we take the limit as q approaches one. It's been a while since I did limits in Calculus, so I'll just take this on faith.
There are presently 69 papers posted on arXiv having "Tsallis entropy" in their titles. What's so important about Tsallis entropy? Boltzmann entropy applies only to systems in equilibrium, and the Boltzmann entropy is an extensive function; that is, it depends on how much matter we have in our system. In non-equilibrium systems we need another way to look at entropy, and now we have Tsallis entropy, which is non-extensive. As can be imagined, a lot of people have a problem with a non-extensive entropy.
q acts merely as a fitting parameter. There's also an argument that Tsallis entropy violates the zeroth law of thermodynamics. That's the law that states that systems in thermal equilibrium with another system are in equilibrium with each other.[3]
In the end, it appears that physicists just need to know whether to apply one entropy or another to a given system. It's not unlike knowing that you should use classical mechanics for bowling balls and quantum mechanics for atoms.[3]
## References:- Constantino Tsallis, "Possible generalization of Boltzmann-Gibbs statistics," Journal of Statistical Physics, vol. 52, nos. 1-2 (July, 1988), pp. 479-487.
- H. V. Ribeiro, E. K. Lenzi, R. S. Mendes, G. A. Mendes, and L. R. da Silva, "Symbolic Sequences and Tsallis Entropy," arXiv Preprint Server, January 16, 2014.
- Jon Cartwright, "Roll over, Boltzmann," Physics World, May, 2014, pp. 31-35.
Linked Keywords: Thermodynamics; scientist; nationality; Sadi Carno (1796-1832); Robert Boyle (1627-1691); William Thomson, Lord Kelvin (1824-1907); James Prescott Joule (1818-1889); Rudolf Clausius (1822-1888); James Clerk Maxwell (1831-1879); Josiah Willard Gibbs (1839-1903); Ludwig Boltzmann (1844-1906); Founders of Thermodynamics; Greece; Western intellectual tradition; philosophy; science; thermodynamics; thermodynamicist; Constantin Carathéodory (1873-1950); profession; mathematics; applied mathematics; axiom; axiomatic; classical mechanics; reversible process; irreversibility; uiform; military dress; youth; Royal Military Academy; Belgium; doctoral advisor; Hermann Minkowski; special relativity; Wikimedia Commons; Boltzmann's entropy formula; Boltzmann entropy; Constantino Tsallis (b. 1943); physicist; naturalization; naturalized citizen; Brazil; Athens; Argentina; doctorate; doctotal degree; physics; University of Paris-Sud; University of Paris-Orsay; chemistry; course; entropy; Boltzmann constant; joule; kelvin; Boltzmann-Gibbs entropy; probability; atom; molecule; correlation; correlated; Tsallis entropy; parameter; limit; Calculus; scientific literature; paper; arXiv; thermodynamic equilibrium; intensive and extensive properties; extensive function; matter; Centro Brasileiro de Pesquisas Físicas; biology; nuclear physics; finance; music; linguistics; nucleic acid sequence; DNA sequence; curve fit; fitting; zeroth law of thermodynamics; physicist; bowling ball; quantum mechanics. |
RSS Feed
## Google Search
Latest Books by Dev Gualtieri
- Voice Synthesis - June 26, 2017
- Refining Germanium - June 22, 2017
- Granular Capillarity - June 19, 2017
- Kirchhoff–Plateau Problem - June 15, 2017
- Self-Assembly - June 12, 2017
- Physics, Math, and Sociology - June 8, 2017
- Graphene from Ethylene - June 5, 2017
- Crystal Alignment Forces - June 1, 2017
- Martian Brickwork - May 29, 2017
- Carbon Nanotube Textile - May 25, 2017
- The Scent of Books - May 22, 2017
- Patterns from Randomness - May 18, 2017
- Terpene - May 15, 2017
- The Physics of Inequality - May 11, 2017
- Asteroid 2015 BZ509 - May 8, 2017
- Fuzzy Fibers - May 4, 2017
- The Sofa Problem - May 1, 2017
- The Wisdom of Composite Crowds - April 27, 2017
- J. Robert Oppenheimer and Black Holes - April 24, 2017
- Modeling Leaf Mass - April 20, 2017
- Easter, Chicks and Eggs - April 13, 2017
- You, Robot - April 10, 2017
- Collisions - April 6, 2017
- Eugene Garfield (1925-2017) - April 3, 2017
- Old Fossils - March 30, 2017
- Levitation - March 27, 2017
- Soybean Graphene - March 23, 2017
- Income Inequality and Geometrical Frustration - March 20, 2017
- Wireless Power - March 16, 2017
- Trilobite Sex - March 13, 2017
- Freezing, Outside-In - March 9, 2017
- Ammonia Synthesis - March 6, 2017
- High Altitude Radiation - March 2, 2017
- C.N. Yang - February 27, 2017
- VOC Detection with Nanocrystals - February 23, 2017
- Molecular Fountains - February 20, 2017
- Jet Lag - February 16, 2017
- Highly Flexible Conductors - February 13, 2017
- Graphene Friction - February 9, 2017
- Dynamic Range - February 6, 2017
- Robert Boyle's To-Do List for Science - February 2, 2017
- Nanowire Ink - January 30, 2017
- Random Triangles - January 26, 2017
- Torricelli's law - January 23, 2017
- Magnetic Memory - January 19, 2017
- Graphene Putty - January 16, 2017
- Seahorse Genome - January 12, 2017
- Infinite c - January 9, 2017
- 150 Years of Transatlantic Telegraphy - January 5, 2017
- Cold Work on the Nanoscale - January 2, 2017
- Holidays 2016 - December 22, 2016
- Ballistics - December 19, 2016
- Salted Frogs - December 15, 2016
- Negative Thermal Expansion - December 12, 2016
- Verbal Cues and Stereotypes - December 8, 2016
- Capacitance Sensing - December 5, 2016
- Gallium Nitride Tribology - December 1, 2016
- Lunar Origin - November 27, 2016
- Pumpkin Propagation - November 24, 2016
- Math Anxiety - November 21, 2016
- Borophene - November 17, 2016
- Forced Innovation - November 14, 2016
- Combating Glare - November 10, 2016
- Solar Tilt and Planet Nine - November 7, 2016
- The Proton Size Problem - November 3, 2016
### Deep ArchiveDeep Archive 2006-2008
Blog Article Directory on a Single Page |

Copyright © 2017 Tikalon LLC, All Rights Reserved.

Last Update: 06-26-2017