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The Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

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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. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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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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Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

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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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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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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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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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Related Experiment Video

Updated: Mar 8, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Stochastic Thermodynamics of Learning.

Sebastian Goldt1, Udo Seifert1

  • 1II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany.

Physical Review Letters
|January 21, 2017
PubMed
Summary

Organisms learn from noisy environments using neural networks. This study shows learning efficiency is limited by thermodynamic costs, with optimal learning conditions discussed.

Area of Science:

  • Computational neuroscience
  • Statistical physics

Background:

  • Organisms process environmental data using neural networks to build internal models.
  • Understanding the physical limits of biological and artificial learning is crucial.

Purpose of the Study:

  • To analyze neural network learning of classification rules using stochastic thermodynamics.
  • To introduce and define a learning efficiency metric.
  • To explore conditions for optimal learning and analyze Hebbian learning.

Main Methods:

  • Application of stochastic thermodynamics principles.
  • Analysis of information acquisition in neural networks.
  • Thermodynamic limit analysis of Hebbian learning.

Main Results:

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  • Information acquired during learning is thermodynamically bounded.
  • A learning efficiency parameter (η ≤ 1) was introduced.
  • Conditions for achieving optimal learning efficiency were identified.

Conclusions:

  • Neural network learning is constrained by thermodynamic costs.
  • The introduced learning efficiency provides a framework for evaluating learning processes.
  • Further analysis of Hebbian learning in the thermodynamic limit offers insights into efficient information processing.