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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 Entropy as a State Function

The Entropy as a State Function

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...

Absolute Entropies and the Third Law of Thermodynamics

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...

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

Entropy

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...

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...

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Related Experiment Video

Updated: Jul 9, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Quantum Rényi α-Entropies for Graph Characterization.

IEEE Transactions on Neural Networks and Learning Systems

|July 7, 2026

Summary

This summary is machine-generated.

This study introduces novel graph kernels using quantum Renyi entropies for efficient and interpretable graph comparison. These methods accurately characterize unlabeled graph structures, outperforming existing techniques.

Related Experiment Videos

Last Updated: Jul 9, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

Graph analytics
Quantum information theory
Machine learning

Background:

Graph structural similarity comparison is crucial but challenging due to graph nonlinearity.
Existing methods often lack expressiveness, interpretability, or computational efficiency for large graphs.

Purpose of the Study:

To propose novel, efficient, and interpretable graph kernels for structural similarity comparison.
To leverage quantum Renyi entropies for characterizing unlabeled graph structures.

Main Methods:

Developed graph kernels based on quantum Renyi alpha-entropies of various orders.
Computed entropies from both unnormalized and normalized Laplacian matrices.
Investigated entropy properties related to substructure frequencies and degree statistics.

Main Results:

The proposed quantum Renyi entropy-based graph kernels are theoretically grounded and interpretable.
These kernels effectively characterize unlabeled graph structures, including paths and cycles.
Experimental results show competitive or superior performance against state-of-the-art methods, including deep learning.

Conclusions:

Novel graph kernels based on quantum Renyi entropies offer an efficient and effective solution for graph structural similarity.
The approach provides interpretable measures and demonstrates strong performance on benchmark datasets.
This work advances graph analytics by integrating quantum principles for robust graph characterization.