Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Thermodynamic stability conditions for nonadditive composable entropies

  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract.

The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not equivalent to the corresponding TSC. It is shown that both the TSC of Tsallis’ entropy and that of the \(\kappa\)-generalized Boltzmann entropy are equivalent to the positivity of the standard heat capacity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Callen, H.B.: Thermodynamics and an Introduction to Thermostatistics, 2nd edn., Wiley New York (1985) Chap. 8

  2. Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479-487 (1988)

    MathSciNet  MATH  Google Scholar 

  3. Kaniadakis, G., Lissia, M., Rapisarda, A. (eds.): Proc. of the international school and workshop on non-extensive thermodynamics and physical applications (NEXT2001). Physica A 305(1-2) (2001)

  4. Ramshaw, J.D.: Thermodynamic stability conditions for the Tsallis and Rényi entropies. Phys. Lett. 198, 119-121 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Rényi, A.: Probability Theory, North-Holland Amsterdam (1970)

  6. Wada, T.: On the thermodynamic stability conditions of Tsallis’ entropy. Phys. Lett. 297, 334-337 (2002)

    Article  MathSciNet  Google Scholar 

  7. Hotta, M., Joichi, I.: Composability and generalized entropy. Phys. Lett. A 262, 302-309 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Abe, S.: General pseudoadditivity of composable entropy prescribed by the existence of equilibrium. Phys. Rev. E 63, 061105 (2001)

    Article  Google Scholar 

  9. Martínez, S., Pennini, F., Plastino, A.: Thermodynamics’ zeroth law in a nonextensive scenario. Physica A 295, 416-424 (2001)

    Google Scholar 

  10. Abe, S.: Heat and entropy in nonextensive thermodynamics: transmutation from Tsallis theory to Rényi-entropy-based theory. Physica A 300, 417-423 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, Q.A., Le Méhauté, A.: Unnormalized nonextensive expectation value and zeroth law of thermodynamics Chaos Solitons Fractals 15, 537-541 (2003)

  12. Kaniadakis, G.: Non-linear kinetics underlying generalized statistics. Physica A 296, 405-425 (2001)

    Article  MATH  Google Scholar 

  13. Kaniadakis, G., Scarfone, A.M.: A new one-parameter deformation of the exponential function Physica A 305, 69-75 (2002)

  14. Kaniadakis, G.: Statistical mechanics in the context of special relativity. Phys. Rev. E 66, 056125 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Ibaraki University, 316-8511, Hitachi, Ibaraki, Japan

    T. Wada

Authors
  1. T. Wada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Wada.

Additional information

Communicated by M. Sugiyama

Received: 29 May 2003, Accepted: 28 August 2003, Published online: 9 December 2003

PACS:

05.20.-y, 05.70.-a, 05.90. + m

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wada, T. Thermodynamic stability conditions for nonadditive composable entropies. Continuum Mech. Thermodyn. 16, 263–267 (2004). https://doi.org/10.1007/s00161-003-0156-y

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-003-0156-y

Keywords:

Search

Navigation