Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Entropy and the Second Law of Thermodynamics

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...

Entropy

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...

Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Third Law of Thermodynamics

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.

Second Law of Thermodynamics

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...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Thermodynamic uncertainty relation for quantum entropy production.

Physical review. E·2024

Same author

Uncertainty relation for symmetric Petz-Rényi relative entropy.

Physical review. E·2024

Same author

Limiting flux in quantum thermodynamics.

Physical review. E·2024

Same author

Improving the Cramér-Rao bound with the detailed fluctuation theorem.

Physical review. E·2024

Same author

Thermodynamic variational relation.

Physical review. E·2023

Same author

Bound for the moment generating function from the detailed fluctuation theorem.

Physical review. E·2023

Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026

Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026

Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026

Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026

Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026

Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 2, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Quantum relative entropy uncertainty relation.

Domingos S P Salazar¹

¹Unidade de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil.

Physical Review. E

|February 17, 2024

Summary

This summary is machine-generated.

We introduce a quantum thermodynamic uncertainty relation bounding quantum observable uncertainty using quantum relative entropy. This advances understanding of fluctuations and entropy production in quantum systems.

More Related Videos

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

Related Experiment Videos

Last Updated: Jul 2, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

Area of Science:

Quantum thermodynamics
Information theory
Statistical mechanics

Background:

The thermodynamic uncertainty relation (TUR) connects current fluctuations to entropy production in classical systems.
Existing TURs often leverage information-theoretic concepts like Kullback-Leibler divergence.
These relations provide fundamental bounds on measurement uncertainty.

Purpose of the Study:

To generalize the thermodynamic uncertainty relation to quantum systems.
To establish a lower bound for the uncertainty of quantum observables.
To derive a quantum version of the entropy production bound.

Main Methods:

Generalizing classical information-theoretic bounds to the quantum realm.
Utilizing quantum relative entropy as a measure of dissimilarity.
Applying derived relations to quantum observables and entropy production.

Main Results:

A novel quantum thermodynamic uncertainty relation is derived.
This relation bounds quantum observable uncertainty by quantum relative entropy.
The result is applicable to arbitrary quantum dynamics and non-thermal environments.

Conclusions:

The study successfully extends the concept of thermodynamic uncertainty to quantum mechanics.
The derived quantum TUR offers new insights into fluctuation-dissipation theorems in quantum systems.
This work provides a foundational tool for analyzing quantum thermodynamics and information processing.