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Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Entropy02:39

Entropy

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...
Entropy01:18

Entropy

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.
Consider an infinitesimal step in the expansion, which...
Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...

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Related Experiment Videos

A stochastic optimization approach to coarse-graining using a relative-entropy framework.

Ilias Bilionis1, Nicholas Zabaras

  • 1Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H.T. Rhodes Hall, Cornell University, Ithaca, New York 14853-3801, USA.

The Journal of Chemical Physics
|February 8, 2013
PubMed
Summary
This summary is machine-generated.

Relative entropy offers a robust method for selecting coarse-grained potentials. New stochastic algorithms address optimization challenges, enhancing applicability in computational modeling.

Related Experiment Videos

Area of Science:

  • Computational chemistry and physics
  • Statistical mechanics
  • Machine learning for scientific discovery

Background:

  • Relative entropy is a principled approach for selecting coarse-grained potentials.
  • Current applications are hindered by optimization problems involving noisy gradients.
  • Deterministic methods require extensive sampling or ad hoc modifications, increasing computational cost or reducing validity.

Purpose of the Study:

  • To develop more applicable methods for using relative entropy in coarse-graining.
  • To overcome the limitations of noisy gradients in optimization problems.
  • To propose alternative optimization schemes for wider adoption of relative entropy.

Main Methods:

  • Development of novel stochastic algorithms for optimization.
  • Application of these algorithms to solve relative entropy-based problems.
  • Comparative analysis against deterministic optimization schemes.

Main Results:

  • Successfully implemented stochastic algorithms to address noisy gradient issues.
  • Demonstrated improved stability and reduced computational demand compared to traditional methods.
  • Validated the effectiveness of the proposed schemes for relative entropy optimization.

Conclusions:

  • The proposed stochastic algorithms significantly enhance the applicability of relative entropy for coarse-grained potential selection.
  • These methods provide a more computationally tractable and reliable framework.
  • Opens new avenues for advanced molecular simulations and materials science.