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Entropy02:39

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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...
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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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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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Space-Time Curvature and the General Theory of Relativity01:17

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In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
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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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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...
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Geometric Interpretation of Timelike Entanglement Entropy.

Michal P Heller1, Fabio Ori1, Alexandre Serantes1

  • 1Ghent University, Department of Physics and Astronomy, 9000 Ghent, Belgium.

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Summary
This summary is machine-generated.

We propose complex extremal surfaces as carriers of holographic timelike entanglement entropy. This offers a new time-centric method to study spacetime emergence in holographic theories.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory

Background:

  • Holographic entanglement entropy (HEE) is a key tool in quantum gravity.
  • Analytic continuations of HEE with timelike boundary subregions offer new insights into spacetime.
  • Understanding the bulk geometric interpretation of these continuations is crucial.

Purpose of the Study:

  • To propose and investigate complex extremal surfaces as the bulk carriers of holographic timelike entanglement entropy.
  • To provide a geometric interpretation for analytic continuations of HEE.
  • To enable the study of holographic timelike entanglement entropy in full generality.

Main Methods:

  • Investigating analytic continuations of holographic spacetimes into complex coordinates.
  • Identifying boundary-anchored extremal surfaces in these complex spacetimes.
  • Studying complex extremal surfaces anchored on a timelike strip in anti-de Sitter black brane boundaries.

Main Results:

  • Proposed complex extremal surfaces as the geometric interpretation of holographic timelike entanglement entropy.
  • Provided a unified geometric understanding of known analytic continuation cases.
  • Identified multiple complex extremal surfaces for a specific boundary configuration.

Conclusions:

  • Complex extremal surfaces offer a powerful geometric framework for holographic timelike entanglement entropy.
  • This approach generalizes the study of time-centric probes of spacetime emergence.
  • Further investigation is needed to identify selection principles for physical contributions.