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Entropy Change in Reversible Processes01:10

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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.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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Entropy01:18

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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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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 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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Maximum-Entropy Inference with a Programmable Annealer.

Nicholas Chancellor1, Szilard Szoke2, Walter Vinci3,4

  • 1London Centre For Nanotechnology 19 Gordon St, London, WC1H 0AH, UK.

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Maximum entropy decoding using programmable annealers slightly improves bit-error rates over maximum likelihood, extracting useful information from excited states for machine learning applications.

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Area of Science:

  • Quantum computing
  • Statistical mechanics
  • Information theory

Background:

  • Optimization problems seek minimum energy configurations, often corrupted by noise.
  • Maximum likelihood assumes noise, while maximum entropy uses Boltzmann distributions to correct for it.

Purpose of the Study:

  • To investigate finite temperature maximum entropy decoding using a programmable annealer.
  • To compare its performance against maximum likelihood for information decoding.
  • To analyze the sampling distribution of the annealer.

Main Methods:

  • Simulating information decoding as a random Ising model in a field.
  • Utilizing a programmable annealer for experimental analysis.
  • Developing a bit-by-bit analytical method for distribution analysis.

Main Results:

  • Finite temperature maximum entropy decoding demonstrated slightly better bit-error rates than maximum likelihood.
  • Experimental results confirmed information extraction from annealer's excited states.
  • The annealer was shown to sample from a highly Boltzmann-like distribution.

Conclusions:

  • Programmable annealers can be effective for maximum entropy inference.
  • These machines show promise for machine learning tasks like language processing and image recognition.
  • Extracting information from excited states is a viable strategy for improving decoding accuracy.