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Related Concept Videos

Calorimetry01:19

Calorimetry

When objects at different temperatures are placed in contact with each other but isolated from everything else, they attain thermal equilibrium. A container that prevents heat transfer in or out is called a calorimeter, and the use of a calorimeter to make measurements is called calorimetry. Generally, these measurements involve heat or specific heat capacity. The term "calorimetry problem" is used for any problem where the specified objects are thermally isolated from their surroundings. An...
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Parameter Estimation as a Problem in Statistical Thermodynamics.

Keith A Earle1, David J Schneider

  • 1Physics Department, University at Albany (SUNY), kearle@albany.edu , http://earlelab.rit.albany.edu.

AIP Conference Proceedings
|September 20, 2011
PubMed
Summary
This summary is machine-generated.

This study connects parameter fitting to statistical thermodynamics using the maximum entropy (maxent) principle. It shows how signal averaging relates to partition functions and interprets fitting errors through thermodynamic concepts, offering a new geometric approach to parameter estimation.

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Area of Science:

  • Statistical Thermodynamics
  • Parameter Estimation
  • Information Theory

Background:

  • Parameter fitting is a crucial but complex process in scientific data analysis.
  • The maximum entropy (maxent) principle provides a powerful framework for statistical inference.
  • Existing methods for combining experimental data and estimating errors can be improved.

Purpose of the Study:

  • To explore the theoretical connections between parameter fitting and statistical thermodynamics.
  • To re-interpret signal averaging and systematic errors within a thermodynamic framework.
  • To develop a novel, geometry-based approach for parameter fitting and error estimation.

Main Methods:

  • Utilized Jaynes' maximum entropy principle as a foundational concept.
  • Developed modified one-particle partition functions to describe signal averaging with variable particle numbers.
  • Interpreted systematic errors as deviations from ideal gas behavior and derived conjugate forces from partition functions.

Main Results:

  • Demonstrated that signal averaging corresponds to an entropy extensive in the number of measurements.
  • Showcased an unbiased method for combining measurements from different experiments to maximize simultaneous fitting entropy.
  • Established a geometric interpretation of parameter space derived from the distribution function, with implications for error estimation.

Conclusions:

  • Parameter fitting can be viewed as a thermodynamic process minimizing free energy or maximizing entropy.
  • Fit parameters can be treated as generalized coordinates, with conjugate forces derived from the system's partition function.
  • The proposed geometric framework offers a pathway for more robust and automated parameter fitting algorithms.