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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 models, the...
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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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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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Stochastic thermodynamics with arbitrary interventions.

Philipp Strasberg1, Andreas Winter1,2

  • 1Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.

Physical Review. E
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Summary
This summary is machine-generated.

This study advances stochastic thermodynamics by incorporating discrete, imperfect measurements and feedback control. It verifies the first law at the trajectory level and the second law on average for driven systems.

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Area of Science:

  • Physics
  • Thermodynamics
  • Statistical Mechanics

Background:

  • Stochastic thermodynamics typically assumes continuous monitoring.
  • Real-world systems often involve discrete and imperfect measurements.
  • Feedback control introduces complex dynamics in thermodynamic processes.

Purpose of the Study:

  • Extend stochastic thermodynamics to discrete and imperfect measurements.
  • Incorporate feedback control dependent on measurement history.
  • Define thermodynamic quantities along causal trajectories for driven systems.

Main Methods:

  • Developed a theoretical framework for discrete, imperfect measurements.
  • Defined internal energy, heat, work, and entropy along causal trajectories.
  • Utilized a classical version of Stinespring's dilation theorem.

Main Results:

  • Verified the first law of thermodynamics at the trajectory level.
  • Confirmed the second law of thermodynamics on average.
  • Derived a general inequality for estimated free energy in Jarzynski-type experiments.
  • Analyzed a Maxwell demon experiment with real-time feedback.

Conclusions:

  • The extended theory accurately describes driven systems with discrete, imperfect measurements and feedback.
  • Provides a unified framework for analyzing complex thermodynamic processes.
  • Offers new insights into information-driven thermodynamics and non-equilibrium statistical mechanics.