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Fisher-based thermodynamics: its Legendre transform and concavity properties
B R Frieden1, A Plastino, A R Plastino
1Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA.
Summary
Fisher's information measure replicates thermodynamics by replacing entropy. This new approach, using Fisher information, successfully treats both equilibrium and nonequilibrium situations similarly to conventional thermodynamics.
Area of Science:
- Thermodynamics
- Information Theory
Background:
- The Legendre-transform structure is fundamental to conventional thermodynamics.
- Entropy (S) is a key concept in describing thermodynamic systems.
Purpose of the Study:
- To explore the replacement of entropy (S) with Fisher's information measure (I) in thermodynamic structures.
- To develop a generalized thermodynamic framework applicable to both equilibrium and nonequilibrium systems.
Main Methods:
- Replicating the Legendre-transform structure of thermodynamics.
- Utilizing Fisher's information measure (I) in place of entropy (S).
- Investigating the concavity property of Fisher's information measure.
Main Results:
- The Legendre-transform structure of thermodynamics is successfully replicated using Fisher's information measure.
- Fisher's information measure (I) exhibits the crucial thermodynamic property of concavity.
- A novel thermodynamic approach is developed that unifies the treatment of equilibrium and nonequilibrium systems.
Conclusions:
- Fisher's information measure provides a viable alternative to entropy in thermodynamic formalisms.
- This information-theoretic approach offers a unified perspective on thermodynamic states, extending beyond equilibrium conditions.