Related Experiment Video
Updated: Aug 22, 2025
09:23
Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
Published on: August 16, 2017
8.2K
Non-Hermitian Generalization of Rényi Entropy
1Department of Physics, College of Science, North China University of Technology, Beijing 100144, China.
Entropy (Basel, Switzerland)
|November 11, 2022
Summary
Researchers developed a generalized Renyi entropy applicable to non-Hermitian systems. This new form accurately describes entropy dynamics even when density matrices are not normalized, overcoming limitations of previous quantum entropy measures.
Area of Science:
- Quantum Information Science
- Thermodynamics
- Non-Hermitian Systems
Background:
- Rényi entropy offers a unified approach to characterizing classical and quantum information properties.
- Conventional quantum Rényi entropy requires normalized density matrices, limiting its application to Hermitian systems.
- Non-Hermitian systems can lead to non-normalized density matrices, posing challenges for standard entropy calculations.
Purpose of the Study:
- To develop a generalized form of Rényi entropy suitable for non-Hermitian systems.
- To extend the applicability of Rényi entropy to scenarios with non-normalized density matrices.
- To accurately describe entropy dynamics in non-Hermitian quantum systems.
Main Methods:
- Introduced a generalized form of the α-Rényi entropy.
- Extended the order parameter α from finite positive real numbers to zero and infinity.
- Developed a method to calculate entropy using both normalized and non-normalized density matrices.
Main Results:
- A concise and generalized form of α-Rényi entropy was obtained.
- The generalized entropy is directly calculable with both normalized and non-normalized density matrices.
- Demonstrated the necessity of the generalization using non-Hermitian detuning two-level systems.
Conclusions:
- The generalized α-Rényi entropy appropriately describes entropy dynamics in non-Hermitian systems.
- This work extends the utility of Rényi entropy to a broader class of quantum systems.
- The findings provide a more robust tool for analyzing quantum information in non-Hermitian contexts.
More Related Videos
Related Concept Videos
01:18Entropy
2.7K
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...
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...
2.7K
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
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
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
19.3K
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.
19.3K
02:49Second Law of Thermodynamics
24.2K
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...
24.2K