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Related Concept Videos

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...
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...
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...
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Anomalous thermodynamics at the microscale.

Antonio Celani1, Stefano Bo, Ralf Eichhorn

  • 1Physics of Biological Systems, Institut Pasteur and CNRS UMR 3525, 28 rue du docteur Roux, 75015 Paris, France.

Physical Review Letters
|February 2, 2013
PubMed
Summary
This summary is machine-generated.

Microscopic particle motion is usually well-described by neglecting inertia. However, this overdamped approximation fails for thermodynamic quantities like entropy production, especially with temperature gradients, revealing an anomalous effect.

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Area of Science:

  • Physics
  • Thermodynamics
  • Statistical Mechanics

Background:

  • Particle motion at the microscale is governed by thermal fluctuations, applied forces, and fluid viscosity.
  • The overdamped approximation, which neglects inertia, accurately describes particle mechanics in many scenarios.
  • Thermodynamic quantities, such as entropy production, are crucial for understanding systems far from equilibrium.

Purpose of the Study:

  • To investigate the validity of the overdamped approximation for thermodynamic quantities in the presence of temperature gradients.
  • To identify and characterize anomalous behavior in entropy production when finite inertia is considered.
  • To explore the underlying mechanisms causing deviations from the overdamped approximation.

Main Methods:

  • Analysis of particle motion in a viscous fluid with temperature gradients.
  • Theoretical investigation in the limit of vanishingly small, yet finite, inertia.
  • Examination of thermodynamic quantities, specifically entropy production.
  • Identification of phase-space trajectories contributing to anomalous entropy production.

Main Results:

  • The overdamped approximation fails dramatically when considering entropy production with temperature gradients.
  • An anomalous contribution to entropy production emerges in the limit of small, finite inertia.
  • This phenomenon, termed 'entropic anomaly,' arises from symmetry breaking.
  • Anomalous entropy production is linked to specific cyclic trajectories in phase space.

Conclusions:

  • Finite inertia, even when small, significantly impacts thermodynamic descriptions of microscale particle motion.
  • The overdamped approximation is insufficient for accurately calculating entropy production in systems with temperature gradients.
  • The discovered entropic anomaly highlights a fundamental limitation of neglecting inertia in certain thermodynamic contexts.