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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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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...
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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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Entropy and the Second Law of Thermodynamics01:26

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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
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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 models, the...
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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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Inferring Entropy Production in Many-Body Systems Using Nonequilibrium Maximum Entropy.

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This summary is machine-generated.

We developed a new method to calculate entropy production in complex systems. This approach overcomes computational limits and works for systems with long memory, offering insights into their thermodynamics.

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Area of Science:

  • Statistical physics
  • Computational thermodynamics
  • Complex systems analysis

Background:

  • Estimating entropy production (EP) in high-dimensional stochastic systems is computationally challenging.
  • Standard methods fail for many-body and non-Markovian systems due to limitations.

Purpose of the Study:

  • To propose a novel method for inferring entropy production in complex systems.
  • To overcome limitations of existing techniques for high-dimensional and non-Markovian systems.

Main Methods:

  • Exploiting a nonequilibrium maximum entropy principle analogue and convex duality.
  • Inferring trajectory-level EP and average EP bounds using trajectory observables.
  • Avoiding reconstruction of probability distributions or rate matrices.

Main Results:

  • Successfully inferred entropy production in a 1000-spin disordered model and neural spike-train data.
  • Developed a method applicable to systems with long memory and without special assumptions.
  • Enabled hierarchical decomposition of EP and provided a thermodynamic uncertainty relation interpretation.

Conclusions:

  • The proposed method offers a tractable approach for calculating entropy production in previously intractable systems.
  • This technique provides new tools for analyzing thermodynamics in complex, nonequilibrium systems.
  • The method is versatile, applicable to diverse systems from physics to neuroscience.