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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...
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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Updated: May 18, 2026

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
09:42

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Published on: January 16, 2016

Uncertainty relations from simple entropic properties.

Patrick J Coles1, Roger Colbeck, Li Yu

  • 1Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA.

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Quantum uncertainty relations, fundamental to quantum theory, are explored through their entropic forms. This study reveals these relations stem from basic properties like the data-processing inequality, applicable across various entropy measures.

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Area of Science:

  • Quantum Information Theory
  • Quantum Foundations
  • Mathematical Physics

Background:

  • Uncertainty relations are fundamental constraints in quantum mechanics, limiting the predictability of outcomes for incompatible measurements.
  • These relations have significant implications for quantum information tasks like cryptography and entanglement verification.
  • Existing formulations often rely on specific entropy measures, potentially limiting their universality.

Purpose of the Study:

  • To investigate and elucidate the entropic formulation of quantum uncertainty relations.
  • To demonstrate that these entropic uncertainty relations can be derived from more general principles.
  • To establish a unified approach applicable to a wide range of entropy measures.

Main Methods:

  • Derivation of entropic uncertainty relations based on fundamental properties of quantum information.
  • Utilizing the data-processing inequality as a key component in the proof.
  • Generalizing the proofs to be independent of the specific mathematical form of the entropy measure.

Main Results:

  • A novel derivation of entropic uncertainty relations is presented.
  • The study shows these relations are direct consequences of the data-processing inequality and other simple properties.
  • The derived relations are shown to hold for multiple types of entropy, including von Neumann, min-, max-, and Rényi entropies.

Conclusions:

  • The entropic uncertainty relations are robust and universally applicable across various quantum entropy measures.
  • The findings simplify the understanding of uncertainty relations and broaden their applicability in quantum information science.
  • This work provides a unified framework for studying entropic uncertainty, enhancing its utility in theoretical and practical quantum applications.