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Unifying Aspects of Generalized Calculus.

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  • 1Wydział Fizyki Technicznej i Matematyki Stosowanej, Politechnika Gdańska, 80-233 Gdańsk, Poland.

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Summary
This summary is machine-generated.

Non-Newtonian calculus offers a unified approach to generalized thermostatistics and information theory. This powerful mathematical framework, though simple, holds significant untapped potential for scientific advancement.

Keywords:
Kolmogorov–Nagumo averagesescort probabilitiesgeneralized entropiesnon-Diophantine arithmeticnon-Newtonian calculus

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Area of Science:

  • Mathematical Physics
  • Information Theory
  • Statistical Mechanics

Background:

  • Generalized thermostatistics and information theory have seen various isolated developments.
  • A unifying mathematical framework has been lacking for these diverse ideas.

Purpose of the Study:

  • To introduce Non-Newtonian calculus as a unifying formalism.
  • To highlight its simplicity and broad applicability.
  • To advocate for its wider adoption and exploration.

Main Methods:

  • Formalism based on Non-Newtonian calculus.
  • Demonstration of its generality across different fields.

Main Results:

  • Non-Newtonian calculus naturally integrates concepts from generalized thermostatistics.
  • It bridges classical and quantum information theory.
  • The formalism is shown to be as accessible as standard calculus.

Conclusions:

  • Non-Newtonian calculus provides a powerful, yet underutilized, tool.
  • Its theoretical potential in physics and information theory is substantial.
  • Further research and application of this calculus are encouraged.