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Related Concept Videos

Control Volume and System Representations01:16

Control Volume and System Representations

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Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach).
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In mechanics, work is done on an object when the force acting on it displaces the object. In thermodynamics, work done on a system can be estimated when the system's volume changes during any thermodynamic process.
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The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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Partition Function for a Volume of Space.

Ted Jacobson1,2, Manus R Visser2

  • 1Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters
|June 16, 2023
PubMed
Summary
This summary is machine-generated.

We calculated the quantum gravity partition function, yielding Bekenstein-Hawking entropy. This result demonstrates the holographic nature of quantum gravity in finite spatial volumes.

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Area of Science:

  • Quantum Gravity
  • Theoretical Physics
  • Cosmology

Background:

  • The quantum gravity partition function is crucial for understanding the Hilbert space of spatial regions.
  • Previous work by Gibbons and Hawking calculated de Sitter entropy for positive cosmological constants.

Purpose of the Study:

  • To evaluate the quantum gravity partition function for a spatial region with a ball topology and fixed proper volume.
  • To generalize the Gibbons-Hawking entropy computation to a broader range of cosmological scenarios.

Main Methods:

  • Leading order saddle point approximation of the quantum gravity partition function.
  • Analysis of a spatial region with ball topology and fixed proper volume.

Main Results:

  • The partition function is the exponential of the Bekenstein-Hawking entropy.
  • The result is reliable within effective field theory, with mild singularities regulated by higher curvature terms.

Conclusions:

  • The study generalizes the Gibbons-Hawking de Sitter entropy calculation.
  • The findings exhibit the holographic nature of nonperturbative quantum gravity in finite volumes.