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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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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 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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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
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Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay.

Sarah A M Loos1,2,3, Simon Hermann4, Sabine H L Klapp1

  • 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.

Entropy (Basel, Switzerland)
|June 2, 2021
PubMed
Summary
This summary is machine-generated.

Time-delayed stochastic systems exhibit complex behaviors. Exponential delays offer the most effective and robust feedback, stabilizing systems and reducing entropic costs.

Keywords:
feedback coolingnon-Markovian dynamicsnon-reciprocal interactionsstochastic delay differential equationsstochastic thermodynamicstime-delayed feedback control

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Area of Science:

  • Physics
  • Thermodynamics
  • Nonlinear Dynamics

Background:

  • Many natural and artificial systems involve time delays.
  • Understanding the impact of delay distribution on system dynamics is crucial.
  • Stochastic systems with feedback control are common in physics and biology.

Purpose of the Study:

  • Investigate the influence of delay distribution on the thermodynamic properties of time-delayed stochastic systems.
  • Analyze the linear stability and heat dissipation in a classical model with Gamma-distributed delays.
  • Identify optimal delay distributions for system stability and reduced entropic costs.

Main Methods:

  • Studied a classical model with white and colored noise.
  • Focused on Gamma-distributed delays, including exponential delay.
  • Analyzed linear stability and thermodynamic properties, including heat dissipation and entropy production.
  • Considered a colloidal particle subject to time-delayed feedback control.

Main Results:

  • Delay distribution significantly impacts system stability; increasing mean delay can either stabilize or destabilize.
  • Negative heat dissipation (refrigerating effect) observed, where delay force extracts energy and entropy from the bath.
  • Exponential delay demonstrated the most pronounced refrigerating effect.
  • Lowest entropic costs and largest stable parameter regions were found for exponential delay.

Conclusions:

  • Delay distribution is a critical factor in the behavior of time-delayed stochastic systems.
  • Exponential delay emerges as the most effective and robust type of delayed feedback for control.
  • The findings have implications for designing stable and efficient feedback control systems in various applications.