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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...

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

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.
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Second Law of Thermodynamics

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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

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Related Experiment Video

Updated: Apr 7, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Dephasing and dissipation in qubit thermodynamics.

J P Pekola¹, Y Masuyama², Y Nakamura^2,3

¹Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 13500, 00076 Aalto, Finland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 15, 2015

Summary

This study shows that qubit dephasing and relaxation preserve fluctuation relations in nonequilibrium thermodynamics. Standard methods focusing only on internal energy fluctuations deviate from these relations.

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Area of Science:

Quantum information science
Non-equilibrium thermodynamics
Statistical mechanics

Background:

Quantum systems experience decoherence, affecting their thermodynamic properties.
The quantum jump approach models individual quantum processes and their stochastic evolution.
Fluctuation relations (FRs) are key concepts in non-equilibrium thermodynamics.

Purpose of the Study:

To analyze the stochastic evolution and dephasing of a qubit using the quantum jump approach.
To investigate the impact of qubit dephasing and relaxation on fluctuation relations.
To compare the quantum jump approach with standard protocols for evaluating FRs.

Main Methods:

Utilizing the quantum jump approach to model individual realizations of inelastic processes.
Analyzing the behavior of a qubit under dephasing and relaxation.
Comparing results from the quantum jump approach with a standard two-measurement protocol.

Main Results:

Dephasing and relaxation of a qubit maintain the integrity of Jarzynski and Crooks fluctuation relations.
Standard protocols focusing solely on internal energy fluctuations show deviations in FRs.
A relationship is established between the average of the exponential of internal energy and qubit relaxation/dephasing rates in the weak dissipation limit.

Conclusions:

The quantum jump approach accurately captures the behavior of fluctuation relations under decoherence.
Qubit decoherence mechanisms significantly influence the validity of fluctuation relations.
Understanding these relationships is crucial for quantum thermodynamics and statistical mechanics.