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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 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 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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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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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...
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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. 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...
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Entanglement Entropy in Two-Dimensional String Theory.

Sean A Hartnoll1, Edward A Mazenc1

  • 1Department of Physics, Stanford University, Stanford, California 94305-4060, USA.

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|October 3, 2015
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Summary
This summary is machine-generated.

Researchers explored entanglement entropy in 2D string theory to understand emergent spacetime and locality. They found short-distance entanglement in the tachyon field, suggesting spacetime has a nonperturbative graininess.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory

Background:

  • Emergent spacetime requires understanding the origin of locality.
  • Entanglement entropy quantifies short-distance entanglement, a key feature of locality.
  • Two-dimensional string theory offers a simplified model for emergent spatial dimensions.

Purpose of the Study:

  • To compute entanglement entropy in 2D string theory.
  • To investigate the relationship between entanglement and emergent locality.
  • To analyze the role of short-distance entanglement in a simplified emergent spacetime.

Main Methods:

  • Utilized large-N matrix quantum mechanics dual to 2D string theory.
  • Performed calculations in the semiclassical limit of weak string coupling.
  • Isolated specific contributions to entanglement entropy.

Main Results:

  • Computed the entanglement entropy for the emergent spacetime.
  • Identified a logarithmically large, finite contribution to entanglement entropy.
  • This contribution is linked to short-distance entanglement of the tachyon field.

Conclusions:

  • Short-distance entanglement of the tachyon field is a crucial feature of emergent spacetime in 2D string theory.
  • The entanglement entropy calculation provides insights into the nature of locality.
  • Results suggest spacetime possesses a nonperturbative "graininess" at short distances.