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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...

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 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...

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...

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Related Experiment Video

Updated: Jul 18, 2026

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Published on: January 16, 2016

Entanglement entropy beyond the free case.

Thomas Barthel¹, Sébastien Dusuel, Julien Vidal

¹Institute for Theoretical Physics C, RWTH Aachen, 52056 Aachen, Germany.

Physical Review Letters

|December 13, 2006

Summary

We developed a new perturbative method to calculate ground state entanglement entropy in interacting quantum systems. This method accurately predicts scaling behavior near quantum critical points, matching numerical findings.

Area of Science:

Quantum Information Theory
Condensed Matter Physics
Many-Body Systems

Background:

Entanglement entropy quantifies quantum correlations in many-body systems.
Understanding entanglement is crucial for characterizing quantum phases of matter, especially at quantum critical points.
Previous methods often struggle with interacting systems and precise scaling predictions.

Purpose of the Study:

To introduce a novel perturbative method for computing ground state entanglement entropy.
To apply this method to a model of interacting spins in a magnetic field.
To analyze the scaling behavior of entanglement entropy at a quantum critical point.

Main Methods:

Development of a perturbative approach to calculate entanglement entropy.

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Last Updated: Jul 18, 2026

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Published on: January 16, 2016

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

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Published on: July 19, 2016

Application to a collective spin model with magnetic field interactions.

Analytical derivation of scaling laws and finite-size corrections.

Main Results:

The entanglement entropy exhibits logarithmic scaling with subsystem size, system size, and anisotropy at the quantum critical point.
Precise determination of scaling prefactors.
Evaluation of the leading finite-size correction term.

Conclusions:

The perturbative method provides accurate analytical predictions for entanglement entropy.
The results offer deep insights into quantum criticality and entanglement scaling in interacting systems.
Strong agreement between analytical predictions and numerical simulations validates the approach.