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The Entropy as a State Function01:14

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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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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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Entanglement entropy flow and the Ward identity.

Vladimir Rosenhaus1, Michael Smolkin2

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We developed equations for entanglement entropy flow, linking Weyl transformations to coupling changes. This confirms the trace Ward identity and expresses entropy for free fields using the energy-momentum tensor.

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Area of Science:

  • Theoretical Physics
  • Quantum Information Theory
  • String Theory

Background:

  • Entanglement entropy quantifies quantum correlations in quantum field theories.
  • Understanding its behavior under transformations is crucial for theoretical physics.

Purpose of the Study:

  • To derive differential equations for entanglement entropy flow.
  • To establish a connection between metric transformations and coupling variations.
  • To apply the formalism to massive free fields.

Main Methods:

  • Derivation of differential equations for entanglement entropy.
  • Analysis of local Weyl transformations and coupling changes.
  • Utilizing the trace Ward identity.

Main Results:

  • Established a relationship between variations in entanglement entropy under Weyl transformations and coupling changes.
  • Demonstrated this relationship is equivalent to the trace Ward identity.
  • Expressed entanglement entropy for massive free fields as a two-point function of the energy-momentum tensor.

Conclusions:

  • The derived formalism provides a new way to study entanglement entropy.
  • The connection to the trace Ward identity offers deeper insights into quantum field theories.
  • The application to free fields validates the utility of the formalism.