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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.
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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...

Second Law of Thermodynamics

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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...

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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The Quantum-Mechanical Model of an Atom

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

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Updated: Mar 8, 2026

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

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Stochastic Inflation as an Open Quantum System.

¹Princeton University, Department of Physics, Princeton, New Jersey 08540, USA.

Physical Review Letters

|March 6, 2026

Summary

This summary is machine-generated.

We reframe stochastic inflation as an open quantum system, treating short-wavelength modes as the environment for long-wavelength modes. This approach yields a Lindblad master equation, offering a more complete description of cosmic inflation dynamics.

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Area of Science:

Cosmology
Quantum Field Theory
Statistical Mechanics

Background:

Starobinsky's stochastic inflation model describes the universe's early expansion.
Treating quantum fields in curved spacetime as open systems is a developing area.
The Schwinger-Keldysh formalism is a powerful tool for non-equilibrium quantum field theory.

Purpose of the Study:

To reinterpret stochastic inflation within the framework of open quantum systems.
To derive an effective theory for the reduced density matrix of long-wavelength modes.
To investigate deviations from de Sitter space and analyze the resulting master equations.

Main Methods:

Applying the Schwinger-Keldysh formalism to quantum fields in an expanding universe.
Systematically tracing out short-wavelength (environmental) modes.
Deriving a Lindblad master equation for the reduced density matrix.

Main Results:

The effective theory reveals a Lindblad master equation governing the long-wavelength modes.
This equation reduces to a Fokker-Planck equation under slow-roll approximations.
The formalism is extended to global de Sitter space, revealing late-time equilibrium conditions.

Conclusions:

Stochastic inflation can be effectively described as an open quantum system.
The derived master and Fokker-Planck equations provide a more comprehensive understanding of inflationary dynamics.
The study highlights the importance of environmental effects in quantum cosmology.