Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Second Law of Thermodynamics02:49

Second Law of Thermodynamics

27.4K
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...
27.4K
Second Law of Thermodynamics00:53

Second Law of Thermodynamics

70.0K
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...
70.0K
The Entropy as a State Function01:14

The Entropy as a State Function

21
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
21
Entropy02:39

Entropy

37.0K
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...
37.0K
Entropy01:18

Entropy

3.7K
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...
3.7K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.3K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.3K

You might also read

Related Articles

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

Sort by
Same author

Machine learning detection of Gaussian steering in continuous-variable systems under data imbalance.

Scientific reports·2025
Same author

Quantum Nonlocality in Any Forked Tree-Shaped Network.

Entropy (Basel, Switzerland)·2022
Same author

Spatially Confined Synthesis of SnSe Spheres Encapsulated in N, Se Dual-Doped Carbon Networks toward Fast and Durable Sodium Storage.

ACS applied materials & interfaces·2022
Same author

A Computable Gaussian Quantum Correlation for Continuous-Variable Systems.

Entropy (Basel, Switzerland)·2021
Same author

Enhenced cell adhesion on collagen I treated parylene-C microplates.

Journal of biomaterials science. Polymer edition·2021
Same author

Nonclassicality by Local Gaussian Unitary Operations for Gaussian States.

Entropy (Basel, Switzerland)·2020

Related Experiment Video

Updated: Mar 7, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.0K

Entropy exchange for infinite-dimensional systems.

Zhoubo Duan1, Jinchuan Hou1

  • 1Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. of China.

Scientific Reports
|February 7, 2017
PubMed
Summary
This summary is machine-generated.

Entropy exchange in infinite-dimensional systems is defined and shown to depend solely on the channel and state. An explicit expression is proposed, establishing new inequalities for entropy. This work compares entropy exchange with entropy change.

More Related Videos

Spin Saturation Transfer Difference NMR SSTD NMR: A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes
11:44

Spin Saturation Transfer Difference NMR SSTD NMR: A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes

Published on: November 12, 2016

18.7K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K

Related Experiment Videos

Last Updated: Mar 7, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.0K
Spin Saturation Transfer Difference NMR SSTD NMR: A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes
11:44

Spin Saturation Transfer Difference NMR SSTD NMR: A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes

Published on: November 12, 2016

18.7K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K

Area of Science:

  • Quantum Information Theory
  • Mathematical Physics
  • Information Theory

Background:

  • The study of entropy and its properties is fundamental in information theory and quantum mechanics.
  • Understanding entropy exchange in complex systems, particularly infinite-dimensional ones, presents unique challenges.

Purpose of the Study:

  • To define and investigate entropy exchange for channels and states in infinite-dimensional systems.
  • To establish fundamental inequalities related to entropy in these systems.
  • To compare entropy exchange with entropy change.

Main Methods:

  • Formal definition of entropy exchange for infinite-dimensional systems.
  • Derivation of an explicit expression for entropy exchange.
  • Establishment of generalized Klein's inequality, subadditivity, and triangle inequality for entropy.

Main Results:

  • Entropy exchange is shown to depend exclusively on the channel and the state.
  • An explicit formula for entropy exchange is derived.
  • New inequalities concerning entropy, including infinite entropy cases, are proven.

Conclusions:

  • The findings provide a rigorous framework for understanding entropy exchange in infinite-dimensional systems.
  • The established inequalities offer new tools for analyzing entropic properties.
  • The comparison between entropy exchange and entropy change deepens the understanding of information flow.