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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

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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

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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.
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Entropy Change in Reversible Processes

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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.
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Entropy and the Second Law of Thermodynamics

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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...

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Related Experiment Video

Updated: May 4, 2026

Magnetic Tweezers for the Measurement of Twist and Torque

Magnetic Tweezers for the Measurement of Twist and Torque

Published on: May 19, 2014

Topological entanglement entropy with a twist.

Benjamin J Brown¹, Stephen D Bartlett², Andrew C Doherty²

¹Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom.

Physical Review Letters

|December 17, 2013

Summary

Topological defects in the toric code model, known as twists, exhibit properties analogous to Ising anyons. Calculations confirm identical quantum dimensions and fusion rules between toric code defects and Ising anyons.

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Area of Science:

Condensed Matter Physics
Quantum Information Theory
Topological Quantum Computation

Background:

Topologically ordered models exhibit exotic properties, including anyonic excitations.
Defects in these models, such as dislocations, can mirror the behavior of anyons.
The toric code model is a prominent example of a topologically ordered system.

Purpose of the Study:

To investigate the relationship between defects and excitations in the toric code model.
To strengthen the analogy between toric code defects (twists) and Ising anyons.
To utilize topological entanglement entropy as a tool for characterizing defects and excitations.

Main Methods:

Explicit mathematical calculations were performed.
Topological entanglement entropy was employed as a diagnostic tool.
Properties of defects and excitations in the toric code were analyzed.

Main Results:

The toric code model with twists and dyon excitations was shown to possess the same quantum dimensions as an Ising anyon model.
The total quantum dimension for both systems was found to be identical.
The fusion rules for the toric code defects and Ising anyons were demonstrated to be the same.

Conclusions:

The analogy between toric code defects and Ising anyons is robustly supported by quantitative analysis.
Topological entanglement entropy effectively characterizes the properties of defects and excitations.
This finding deepens our understanding of topological order and its emergent phenomena.