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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...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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...

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.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

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: Jul 24, 2025

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

Rényi Entropy, Signed Probabilities, and the Qubit.

Adam Brandenburger¹, Pierfrancesco La Mura², Stuart Zoble³

¹Stern School of Business, Tandon School of Engineering, NYU Shanghai, New York University, New York, NY 10012, USA.

Entropy (Basel, Switzerland)

|July 8, 2023

Summary

This summary is machine-generated.

This study characterizes qubit states using an entropic uncertainty principle on a phase space. It employs Rényi entropy to define quantum mechanics, advancing foundational quantum information science.

Keywords:

Rényi entropy qubit signed probability uncertainty principle

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Last Updated: Jul 24, 2025

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

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Published on: September 5, 2019

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Area of Science:

Quantum Information Science
Quantum Mechanics Foundations
Mathematical Physics

Background:

Qubit states are fundamental to quantum information.
Axiomatizing quantum mechanics requires characterizing these states.
Existing frameworks may benefit from novel mathematical approaches.

Purpose of the Study:

To characterize qubit states within quantum mechanics.
To contribute to the axiomatization of quantum mechanics.
To explore the application of entropic uncertainty principles.

Main Methods:

Utilized an eight-point phase space formulation.
Employed Rényi entropy, a generalization of Shannon entropy.
Defined entropy for signed phase-space probability distributions.

Main Results:

Successfully characterized qubit states using the entropic uncertainty principle.
Demonstrated the utility of Rényi entropy in this context.
Provided a new perspective on quantum state representation.

Conclusions:

The entropic uncertainty principle offers a powerful tool for characterizing quantum states.
Rényi entropy is suitable for analyzing signed phase-space distributions.
This work advances the axiomatization program in quantum mechanics.