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Related Concept Videos

The Entropy as a State Function01:14

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...
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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.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
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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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Systems in mechanical equilibrium exert equal pressure on the separating wall. Similarly, systems in thermal equilibrium share a common thermodynamic property: temperature.Temperature is a measure of the average kinetic energy of particles within a system. More generally, it reflects the internal energy state of the system. The higher the temperature, the more energy a system has, given that other variables, such as volume and pressure, remain constant. However, temperature is not a form of...
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The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated with a wave is called its power, which is total energy divided by the time it takes to transfer the energy. For a sinusoidal wave, energy and power are proportional to the square of both the amplitude and the angular frequency.
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In an electrical system with a resistor, voltage and current signals facilitate the measurement of power and energy across the resistor. For a continuous-time signal, the total energy over a time interval is defined as the integral of the square of the signal's magnitude over that interval. Mathematically, this is expressed as:
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Entropy vs. Energy Waveform Processing: A Comparison Based on the Heat Equation.

Michael S Hughes1, John E McCarthy2, Paul J Bruillard1

  • 1Pacific Northwest National Laboratory, 902 Battelle Blvd., Richland, WA 99354, USA.

Entropy (Basel, Switzerland)
|April 26, 2016
PubMed
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Information imaging, using wave entropy, offers advantages over conventional energy imaging. Joint entropy with an optimal reference signal provides superior sensitivity for detecting subtle changes in scientific observations.

Keywords:
entropy imageinformation wavejoint entropyoptimal detection

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Area of Science:

  • Physics
  • Information Theory
  • Signal Processing

Background:

  • Modern imaging relies on wave energy for pixel values, creating 'energy' pictures.
  • Waves also contain 'information,' quantifiable by entropy, enabling 'information' imaging.

Purpose of the Study:

  • To explore the advantages of information imaging over conventional methods.
  • To identify the most sensitive information measure for imaging applications.

Main Methods:

  • Utilizing joint entropy of collected waves and a reference signal.
  • Defining sensitivity as mean variation divided by mean variance (noise).
  • Employing Wiener integration and heat equation solutions for value computation.

Main Results:

  • Joint entropy demonstrates greater variation and lower variance compared to signal energy.
  • An optimal reference signal for joint entropy was identified and validated.
  • Information imaging shows enhanced sensitivity in experimental observations.

Conclusions:

  • Information imaging, particularly using joint entropy, offers superior performance over energy-based imaging.
  • The developed methods provide a framework for optimizing information imaging sensitivity.
  • This approach has been validated in multiple experimental studies.