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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.
Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

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...
Second Law of Thermodynamics00:53

Second Law of Thermodynamics

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 chemical energy...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Smoluchowski dynamics and the ergodic-nonergodic transition.

Gene F Mazenko1

  • 1The James Franck Institute and the Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 24, 2011
PubMed
Summary

This study investigates ergodic-nonergodic transitions in classical particle systems using Smoluchowski dynamics. An ergodic-nonergodic transition was found at a physically inaccessible packing fraction for hard spheres.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Computational Physics

Background:

  • Classical particle systems exhibit complex dynamics near phase transitions.
  • Understanding liquid-glass transitions is crucial in condensed matter physics.
  • Smoluchowski dynamics provides a framework for modeling Brownian motion.

Purpose of the Study:

  • To investigate ergodic-nonergodic (ENE) transitions in systems driven by Smoluchowski dynamics.
  • To explore the relationship between ENE transitions and the liquid-glass transition.
  • To apply a new theory for the kinetics of classical particle systems.

Main Methods:

  • Developed a self-consistent perturbation theory up to second order in an effective two-body potential.
  • Utilized the Percus-Yevick approximation for the static structure factor of hard spheres.
  • Analytically determined the ergodic-nonergodic equation for the ergodicity function.

Main Results:

  • An ergodic-nonergodic transition was identified for packing fractions greater than η(*)=0.76.
  • This critical packing fraction is physically inaccessible under normal conditions.
  • Demonstrated the existence and utility of a linear fluctuation-dissipation theorem.

Conclusions:

  • The study reveals an ergodic-nonergodic transition in hard sphere systems within the Smoluchowski dynamics framework.
  • The transition occurs at a high, physically unattainable density, suggesting limitations for direct experimental observation.
  • The employed theoretical framework and fluctuation-dissipation theorem offer valuable insights into system dynamics.