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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...

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...

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...

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.

Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...

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: May 30, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Quantum-state reconstruction by maximizing likelihood and entropy.

Yong Siah Teo¹, Huangjun Zhu, Berthold-Georg Englert

¹Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore.

Physical Review Letters

|July 30, 2011

Summary

This summary is machine-generated.

Reconstructing quantum states from limited data is challenging. This study introduces a method maximizing likelihood and entropy to find the most probable and least biased quantum state estimator.

Related Experiment Videos

Last Updated: May 30, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

Quantum information science
Quantum mechanics
Statistical inference

Background:

Quantum-state reconstruction often lacks uniqueness due to incomplete measurements.
Limited data in quantum systems poses challenges for accurate state determination.

Purpose of the Study:

To develop a systematic quantum-state reconstruction scheme for incomplete measurement data.
To identify the most likely and least biased quantum state estimator.
To reconcile partial knowledge with uncertainty in quantum ensembles.

Main Methods:

Derivation of a reconstruction scheme.
Simultaneous maximization of likelihood and von Neumann entropy functionals.
Selection of the most-likely estimator with the largest entropy (least-bias estimator).

Main Results:

A novel reconstruction scheme is derived.
The scheme yields a unique, least-biased estimator consistent with measurement data.
The method effectively balances knowledge and ignorance about the quantum ensemble.

Conclusions:

The proposed method provides a robust approach to quantum-state reconstruction with incomplete data.
Maximizing likelihood and entropy offers a principled way to select the best quantum state estimator.
This technique enhances the understanding and characterization of quantum systems from limited experimental information.