Thermodynamic and Differential Entropy Under a Change of Variables

Details

• Personal Author:
  Gilson MK ; Hnizdo, Vladimir
• Description:
  The differential Shannon entropy of information theory can change under a change of variables (coordinates), but the thermodynamic entropy of a physical system must be invariant under such a change. This difference is puzzling, because the Shannon and Gibbs entropies have the same functional form. We show that a canonical change of variables can, indeed, alter the spatial component of the thermodynamic entropy just as it alters the differential Shannon entropy. However, there is also a momentum part of the entropy, which turns out to undergo an equal and opposite change when the coordinates are transformed, so that the total thermodynamic entropy remains invariant. We furthermore show how one may correctly write the change in total entropy for an isothermal physical process in any set of spatial coordinates. [Description provided by NIOSH]
• Subjects:
  Energy Metabolism Occupational Health Safety
• Keywords:
  Analytical-methods Author Keywords: Thermodynamic Entropy Canonical Transformation Energy-metabolism Jacobian Mathematical-models Non-Cartesian Coordinates Shannon Entropy Spatial Entropy Standards Statistical-analysis Thermodynamic-reactions Thermodynamics

  More +
• ISSN:
  1099-4300
• Document Type:
  Text
• Genre:
  Journal Article
• Place as Subject:
  OSHA Region 3 ; West Virginia
• CIO:
  National Institute for Occupational Safety and Health (NIOSH)
• Division:
  HELD - Health Effects Laboratory Division
• Topic:
  Workplace Safety & Health
• Location:
  North America
• Volume:
  12
• Issue:
  3
• NIOSHTIC Number:
  nn:20036555
• Citation:
  Entropy 2010 Mar; 12(3):578-590
• Contact Point Address:
  Vladimir Hnizdo, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, WV 26505
• Email:
  vhnizdo@cdc.gov
• Federal Fiscal Year:
  2010
• Peer Reviewed:
  True
• Source Full Name:
  Entropy
• Collection(s):
  National Institute for Occupational Safety and Health
• Main Document Checksum:
  urn:sha-512:5cf4253263d6cb094b671fa2044a7883193069ce986c7933c54c5cc44900c5d214cd15a1506d31bf12635f24d0a703506cbe84ead73b4dab4caad00978d2f91c
• Download URL:
  https://stacks.cdc.gov/view/cdc/187927/cdc_187927_DS1.pdf
• File Type:
  [PDF - 131.83 KB ]