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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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A spontaneous process is one that occurs naturally under certain conditions. A nonspontaneous process, on the other hand, will not take place unless it is “driven” by the continual input of energy from an external source. Processes have a natural tendency to occur in one direction under a given set of conditions. Water will naturally flow downhill (spontaneous process), but uphill flow (nonspontaneous process) requires outside intervention such as the use of a pump. Iron exposed to...
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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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Not All Fluctuations Are Created Equal: Spontaneous Variations in Thermodynamic Function.

James P Crutchfield1, Cina Aghamohammadi1

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|November 27, 2024
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Summary
This summary is machine-generated.

This study introduces functional fluctuation theory for nanoscale thermodynamic systems. It reveals that systems often exhibit multiple simultaneous functions, challenging the idea of a single operational mode.

Keywords:
Information Processing Second Law of ThermodynamicsMaxwell’s Demonentropy ratefluctuation relationsfluctuation spectruminformation ratchetlarge deviation theorynonequilibrium steady statethermodynamic formalism

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Information Theory
  • Nanoscale Systems

Background:

  • Understanding the behavior of complex thermodynamic systems, especially at the nanoscale, is crucial for advancements in various scientific fields.
  • Current models often simplify system operations, potentially overlooking crucial functional aspects during fluctuations.
  • The interplay between information processing and thermodynamics is key to deciphering system functionality.

Purpose of the Study:

  • To develop a comprehensive theory of functional fluctuations in thermodynamic systems.
  • To describe system operations across typical and atypical behaviors, encompassing the full spectrum of fluctuations.
  • To provide a framework for determining functionality in complex, memoryful environments.

Main Methods:

  • Utilizing the information processing second law to identify functionality in atypical system realizations.
  • Employing the large-deviation rate function to calculate the probabilities of distinct functional modalities.
  • Extending theoretical frameworks to accommodate highly correlated and memoryful systems and environments.

Main Results:

  • Macroscopic functioning identified across typical and atypical thermodynamic system behaviors.
  • A method to determine functionality for atypical realizations using the information processing second law.
  • Calculation of distinct modality probabilities via an extended large-deviation rate function.

Conclusions:

  • The developed functional fluctuation theory provides a complete description for complex nanoscale thermodynamic systems.
  • Ascribing a single functional modality can be misleading, masking simultaneous, parallel functional transformations.
  • This theory redefines our understanding of biological processes, engineering design, and evolutionary adaptation.