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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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The Entropy as a State Function

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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...

Third Law of Thermodynamics

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Entropy and the Second Law of Thermodynamics

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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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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Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

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Interior Microstates and Black Hole Entropy.

Martin Sasieta¹

¹Leinweber Institute for Theoretical Physics, University of California, Berkeley, CA 94720, USA.

Entropy (Basel, Switzerland)

|May 4, 2026

Summary

This review explores black hole interior microstates in semiclassical gravity. It assesses constructions in AdS/CFT and wormholes to resolve overcounting and explain black hole entropy via state counting.

Keywords:

ads/cft black hole entropy black hole microstates black holes gravitational path integral holography quantum gravity string theory

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Area of Science:

Theoretical Physics
Quantum Gravity
String Theory

Background:

Semiclassical gravity allows numerous black hole interior states, posing a challenge for identifying fundamental quantum microstates.
Understanding black hole entropy requires a precise accounting of these microstates.

Purpose of the Study:

To review explicit constructions of black hole interior microstates.
To assess if these microstates form bases for the black hole Hilbert space.
To investigate how non-perturbative effects resolve microstate overcounting and explain black hole entropy.

Main Methods:

Surveying constructions of black hole interior microstates within AdS2 holography and AdS/CFT correspondence.
Analyzing the role of spacetime wormholes (non-perturbative effects) in the gravitational path integral.
Evaluating microstate counting for reproducing black hole entropy.

Main Results:

Several candidate black hole interior microstate constructions are presented.
The assessment of whether these constructions form complete bases for the black hole Hilbert space is discussed.
The contribution of spacetime wormholes to resolving overcounting and reproducing entropy is highlighted.

Conclusions:

Identifying the correct set of black hole microstates is crucial for a complete theory of quantum gravity.
AdS/CFT and related holographic techniques offer promising avenues for constructing and understanding these microstates.
Non-perturbative gravitational effects are essential for a consistent description of black hole entropy.