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Entropy02:39

Entropy

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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.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Second Law of Thermodynamics02:49

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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...
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Second Law of Thermodynamics00:53

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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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Entropy and the Second Law of Thermodynamics01:20

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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Combining experiments and simulations using the maximum entropy principle.

Wouter Boomsma1, Jesper Ferkinghoff-Borg2, Kresten Lindorff-Larsen1

  • 1Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark.

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Summary
This summary is machine-generated.

The maximum entropy principle helps reconcile computational biology models with experimental data. This method improves quantitative agreement in fields like molecular simulations, addressing discrepancies from model limitations.

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Area of Science:

  • Computational Biology
  • Statistical Mechanics

Background:

  • Comparing computational models with experimental data is crucial in computational biology.
  • Discrepancies often arise between model predictions and experimental results, hindering progress.
  • Existing methods for reconciling these differences lack a general consensus.

Purpose of the Study:

  • Introduce the principle of maximum entropy as a tool for computational biology.
  • Demonstrate its application in addressing quantitative disagreements between models and experiments.
  • Highlight recent advancements in applying maximum entropy to molecular simulations.

Main Methods:

  • Explanation of the maximum entropy principle with a simple example.
  • Application of the method to molecular simulations, particularly in refining potential energy functions.
  • Review of recent studies utilizing maximum entropy for model-experiment reconciliation.

Main Results:

  • Maximum entropy provides a principled approach to construct probability distributions when models conflict with data.
  • Recent studies show its efficacy in molecular simulations by perturbing potential energy functions towards experimental data.
  • These methods offer new theoretical and practical insights for improving model accuracy.

Conclusions:

  • The maximum entropy principle is a valuable and increasingly adopted tool in computational biology.
  • It offers a robust framework for integrating experimental data into computational models.
  • Further research is needed to address remaining challenges and expand its applications.