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

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...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

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.

The Second Law of Thermodynamics

The 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. 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...

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

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.

You might also read

Related Articles

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

Sort by

Same author

Networked SIRS model with Kalman filter state estimation for epidemic monitoring in Europe.

Communications medicine·2026

Same author

Performance evaluation of RespiCast ensemble forecasts for primary care syndromic indicators of viral respiratory disease in Europe.

medRxiv : the preprint server for health sciences·2026

Same author

Dynamic gene regulatory network inference from single-cell data using optimal transport.

Bioinformatics (Oxford, England)·2025

Same author

Unlocking gene regulatory networks for crop resilience and sustainable agriculture.

Nature biotechnology·2025

Same author

Multiomics approaches disclose very-early molecular and cellular switches during insect-venom allergen-specific immunotherapy: an observational study.

Nature communications·2024

Same author

Towards automatic home-based sleep apnea estimation using deep learning.

NPJ digital medicine·2024

Search research articles

Related Experiment Video

Updated: Aug 30, 2025

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

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

Published on: December 4, 2017

Rényi Entropy in Statistical Mechanics.

Jesús Fuentes¹, Jorge Gonçalves^1,2

¹Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, L-4367 Luxembourg, Luxembourg.

Entropy (Basel, Switzerland)

|August 26, 2022

Summary

Rényi entropy naturally emerges from statistical mechanics as the average rate of change of free energy. This concept extends to non-isothermal processes, revealing connections to relative free energy and information divergence measures.

Keywords:

Helmholtz free energy Rényi entropy non-equilibrium thermodynamics relative free energy statistical mechanics

More Related Videos

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Published on: January 16, 2016

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Published on: May 29, 2018

Related Experiment Videos

Last Updated: Aug 30, 2025

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

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

Published on: December 4, 2017

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Published on: January 16, 2016

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Bulk and Thin Film Synthesis of Compositionally Variant Entropy-stabilized Oxides

Published on: May 29, 2018

Area of Science:

Statistical Mechanics
Information Theory
Thermodynamics

Background:

Rényi entropy, a generalization of Shannon entropy, has been explored for statistical mechanics.
Previous attempts to generalize statistical mechanics using Rényi entropy often lacked physical grounding.

Purpose of the Study:

To demonstrate that Rényi entropy naturally arises within statistical mechanics without artificial modifications.
To extend the understanding of Rényi entropy to non-isothermal and isospectral processes.

Main Methods:

Analyzing the relationship between Rényi entropy and the rate of change of free energy over ensembles at varying temperatures.
Investigating generalized free energy distributions for isospectral, non-isothermal processes.

Main Results:

Rényi entropy is shown to be the average rate of change of free energy with respect to temperature.
Relative free energy formulations for non-isothermal processes incorporate Kullback-Leibler divergence and relative Rényi entropy.

Conclusions:

Statistical mechanics does not require modification to naturally incorporate Rényi entropy.
The framework unifies thermodynamic potentials and information-theoretic measures for generalized processes.