Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry

  • Seyed Ali Hosseini Mansoori
  • Behrouz Mirza
  • Mohamadreza Fazel
Open Access
Regular Article - Theoretical Physics


As an extension to our earlier work [1], we employ the Nambu brackets to prove that the divergences of heat capacities correspond to their counterparts in thermodynamic geometry. We also obtain a simple representation for the conformal transformations that connect different thermodynamics metrics to each other. Using our bracket approach, we obtain interesting exact relations between the Hessian matrix with any number of parameters and specific heat capacities. Finally, we employ this approach to investigate some thermodynamic properties of the Meyers-Perry black holes with three spins.


Black Holes Differential and Algebraic Geometry Statistical Methods 2D Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Seyed Ali Hosseini Mansoori
    • 1
  • Behrouz Mirza
    • 1
  • Mohamadreza Fazel
    • 2
  1. 1.Department of PhysicsIsfahan University of TechnologyIsfahanIran
  2. 2.Department of PhysicsUniversity of New MexicoAlbuquerqueUnited States

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