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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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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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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic...
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Stochastic Entropy Production for Classical and Quantum Dynamical Systems with Restricted Diffusion.

Jonathan Dexter1, Ian J Ford1

  • 1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.

Entropy (Basel, Switzerland)
|April 26, 2025
PubMed
Summary
This summary is machine-generated.

This study presents a novel method for calculating stochastic entropy production in systems with restricted phase space diffusion. The approach overcomes mathematical challenges, enabling analysis of complex systems like quantum states.

Keywords:
open quantum system dynamicsstochastic entropy productionstochastic thermodynamics

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Area of Science:

  • Statistical physics
  • Quantum mechanics
  • Stochastic processes

Background:

  • Stochastic entropy production quantifies uncertainty growth in dynamical systems.
  • Mathematical challenges arise when diffusion is confined to lower-dimensional subspaces, complicating Itô process applications.
  • These challenges occur with conserved quantities or when coordinate numbers exceed independent noise sources.

Purpose of the Study:

  • To develop a method for computing stochastic entropy production in systems with restricted phase space diffusion.
  • To illustrate the proposed method with a diffusion-on-an-ellipse model.
  • To apply the method to an open three-level quantum system.

Main Methods:

  • Developed a technique to overcome mathematical difficulties in stochastic entropy production calculations for restricted diffusion.
  • Applied the method to a simplified model of diffusion on an ellipse.
  • Utilized Markovian quantum state diffusion to model an open three-level quantum system.

Main Results:

  • Successfully computed stochastic entropy production despite phase space restrictions.
  • Demonstrated the method's efficacy using a diffusion-on-an-ellipse example.
  • Established conditions for a nonequilibrium stationary state with constant mean stochastic entropy production in a quantum system.

Conclusions:

  • The developed method effectively computes stochastic entropy production in systems with restricted diffusion.
  • The approach is applicable to both classical and quantum systems, including open quantum systems.
  • Environmental couplings can establish nonequilibrium stationary states with stable entropy production rates.