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Thermodynamic Systems01:06

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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
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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. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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Entropy02:39

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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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Entropy01:18

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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Thermodynamics of structure-forming systems.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • Structure-forming systems, from atomic to colloidal scales, are fundamental in nature.
  • Understanding the thermodynamics governing these systems, particularly self-assembly, is crucial.
  • Existing models like Boltzmann-Gibbs entropy may not fully capture the complexities of clustered states.

Purpose of the Study:

  • To derive a novel entropy formulation for structure-forming systems.
  • To investigate the thermodynamic behavior of these systems, especially concerning clustered states.
  • To extend fluctuation theorems to structure-forming systems and explore their applicability.

Main Methods:

  • Derivation of a modified entropy formula incorporating clustered states.
  • Analysis of system behavior across different scales (large vs. small systems) and concentrations.
  • Application of fluctuation theorems, including detailed fluctuation and Crooks' work fluctuation theorems.
  • Modeling of specific physical systems like patchy particles and the Curie-Weiss model.

Main Results:

  • A new entropy formula is derived, differing from Boltzmann-Gibbs entropy by a term for clustered states.
  • The derived entropy shows equivalence to the grand-canonical ensemble for large systems/low concentrations but significant deviations for small systems.
  • Detailed fluctuation and Crooks' work fluctuation theorems are established for these systems.
  • Phase diagrams for patchy particles and phase transitions in the Curie-Weiss model are presented.

Conclusions:

  • The developed thermodynamic framework accurately describes structure-forming systems, particularly those with clustered states.
  • The findings provide new insights into the statistical mechanics of self-assembly and phase transitions.
  • The derived theorems and models offer valuable tools for analyzing diverse physical and chemical systems.