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Entropy production given constraints on the energy functions
Artemy Kolchinsky1, David H Wolpert1
1Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
Physical Review. E
|October 16, 2021
Summary
Driving finite-state systems to desired states with minimal entropy production (EP) is achievable with limited energy function control. A simple condition, based on state probabilities and energy function properties, guarantees successful transformations.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Control Theory
Background:
- Controlling classical systems between probability distributions is crucial in various fields.
- Minimizing entropy production (EP) is a key goal for efficient state transformations.
- Existing methods often require extensive control over system energy functions.
Purpose of the Study:
- To determine the minimal conditions for driving a finite-state system between distributions with vanishing entropy production (EP).
- To establish a condition for achieving state transformations using limited energy function control.
- To derive a lower bound for EP under more general constraints.
Main Methods:
- Derivation of a condition based on state probabilities and graph-theoretic properties of the energy function.
- Analysis of the sufficiency of limited energy function control (e.g., one-dimensional parameter control).
- Formulation of a convex optimization problem to establish EP lower bounds.
Main Results:
- A simple condition guarantees vanishing EP transformations with limited energy function control.
- Minimal control, such as adjusting a single state's energy, is sufficient for many transformations.
- A lower bound on EP is derived for general transition rate constraints.
Conclusions:
- Achieving efficient state transformations in classical systems requires less energy function control than previously thought.
- The derived condition provides a practical guideline for designing control protocols.
- The findings have implications for fields requiring precise control of probabilistic systems.
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