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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 and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...

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...

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 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.

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Related Experiment Video

Updated: May 20, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Quantum channels and their entropic characteristics.

A S Holevo¹, V Giovannetti

¹Steklov Mathematical Institute, Gubkina 8, 119991 Moscow, Russia. holevo@mi.ras.ru

Reports on Progress in Physics. Physical Society (Great Britain)

|July 14, 2012

Summary

Quantum information theory introduces quantum channels for data processing. This survey explores their properties, entropic characterization, and the role of entanglement as a communication resource.

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Area of Science:

Quantum Information Theory
Quantum Optics

Background:

Quantum channels are fundamental to quantum information theory, enabling data transmission and processing.
The development of quantum channels led to entropic quantities like channel capacities, which measure information-processing performance.

Purpose of the Study:

To survey the main properties of quantum channels.
To explore their entropic characterization and capacity formulae.
To highlight the role of entanglement in quantum communication.

Main Methods:

Review of theoretical concepts in quantum channel theory.
Analysis of entropic quantities and channel capacity formulas.
Discussion of finite-dimensional and continuous-variable quantum systems.

Main Results:

Detailed properties of quantum channels are presented.
Entropic characterization and capacity formulas are explained with examples.
The significance of entanglement as a quantum communication resource is emphasized.

Conclusions:

Quantum channels are key components in quantum information processing.
Entropic quantities provide crucial metrics for channel performance.
Entanglement is a vital resource for advanced quantum communication protocols.