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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.
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Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...
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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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Entropy Evolution in Consensus Networks.

Shuangshuang Fu1, Guodong Shi2, Ian R Petersen3

  • 1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China.

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|May 10, 2017
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Summary
This summary is machine-generated.

We studied network entropy in classical and quantum consensus dynamics. Classical network entropy non-increases, while quantum network entropy non-decreases, revealing a key difference between systems.

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Area of Science:

  • Network science
  • Quantum information theory
  • Statistical mechanics

Background:

  • Consensus dynamics are crucial for distributed systems, aiming for agreement among nodes.
  • Network entropy quantifies information distribution and disorder within a network.
  • Classical and quantum systems exhibit distinct information processing capabilities.

Purpose of the Study:

  • To investigate and compare the evolution of network entropy in classical and quantum consensus dynamics.
  • To analyze the behavior of differential entropy in classical networks and von Neumann entropy in quantum networks.
  • To identify relationships between classical and quantum distributed algorithms.

Main Methods:

  • Analysis of consensus dynamics in both classical and quantum network models.
  • Mathematical formulation and comparison of network differential entropy and von Neumann entropy.
  • Comparative study of distributed algorithms with varying coefficients (random/deterministic) in classical and quantum settings.

Main Results:

  • Classical network differential entropy is monotonically non-increasing for continuous random initial values.
  • Quantum network von Neumann entropy is monotonically non-decreasing.
  • Quantum algorithms with deterministic coefficients show a physical correspondence to classical algorithms with random coefficients.

Conclusions:

  • A fundamental divergence in entropy evolution exists between classical and quantum consensus dynamics.
  • The choice of coefficients (random vs. deterministic) in distributed algorithms significantly impacts network entropy behavior.
  • Quantum and classical distributed algorithms can exhibit analogous behaviors under specific conditions, offering insights into cross-platform information dynamics.