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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...

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 Second Law of Thermodynamics

The Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be put...

Second Law of Thermodynamics

Second Law of Thermodynamics

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: May 27, 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

Nonequilibrium entropy production for open quantum systems.

Sebastian Deffner¹, Eric Lutz

¹Department of Physics, University of Augsburg, D-86135 Augsburg, Germany.

Physical Review Letters

|November 24, 2011

Summary

This summary is machine-generated.

We derived exact formulas for entropy production in driven quantum systems, even far from equilibrium. This work generalizes fluctuation theorems for open quantum systems using energy measurement statistics.

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Area of Science:

Quantum thermodynamics
Statistical mechanics
Non-equilibrium physics

Background:

Understanding entropy production is crucial for characterizing irreversible processes in quantum systems.
Current theories often rely on approximations or are limited to near-equilibrium conditions.

Purpose of the Study:

To derive exact microscopic expressions for entropy production and its rate in open quantum systems.
To generalize fluctuation theorems for systems arbitrarily far from equilibrium.

Main Methods:

Considering open quantum systems weakly coupled to a heat reservoir.
Analyzing systems driven by arbitrary time-dependent parameters.
Utilizing two-point energy measurement statistics of the system and reservoir.

Main Results:

Exact microscopic expressions for nonequilibrium entropy production and entropy production rate were derived.
The derived expressions are valid arbitrarily far from thermodynamic equilibrium.
A quantum generalization of Seifert's integrated fluctuation theorem was obtained.

Conclusions:

The study provides exact, non-perturbative results for entropy production in driven open quantum systems.
The findings extend the applicability of fluctuation theorems to strongly non-equilibrium regimes.
This work offers a powerful theoretical framework for analyzing quantum thermodynamics beyond equilibrium.