Related Experiment Video
Updated: Aug 30, 2025
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
8.6K
Rényi Entropy in Statistical Mechanics.
Jesús Fuentes1, Jorge Gonçalves1,2
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.
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.
Related Concept Videos
01:20Entropy and the Second Law of Thermodynamics
3.0K
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...
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...
3.0K
02:39Entropy
30.8K
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...
30.8K
01:10Entropy Change in Reversible Processes
2.7K
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 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.
2.7K
01:14The Second Law of Thermodynamics
5.5K
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...
5.5K
03:00Standard Entropy Change for a Reaction
20.8K
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.
20.8K
02:38Third Law of Thermodynamics
19.4K
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.
19.4K