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Optimal protocols and optimal transport in stochastic thermodynamics
Erik Aurell1, Carlos Mejía-Monasterio, Paolo Muratore-Ginanneschi
1ACCESS Linnaeus Centre, KTH, Stockholm, Sweden. eaurell@kth.se
Physical Review Letters
|July 21, 2011
Summary
Optimization problems in small system thermodynamics are solved using optimal transport methods. This approach, particularly the Burgers equation, efficiently minimizes heat and work during nonequilibrium transitions.
Area of Science:
- Statistical physics
- Thermodynamics of small systems
Background:
- Small systems are increasingly important in statistical physics.
- Controlling and optimizing nonequilibrium processes in these systems is a key challenge.
Purpose of the Study:
- To demonstrate that optimal transport theory provides a framework for solving optimization problems in small system thermodynamics.
- To extend the range of solvable optimization problems in this field.
Main Methods:
- Applying deterministic optimal transport theory to thermodynamic control problems.
- Utilizing the Burgers equation and its associated velocity field for mass transport and minimizing energy dissipation.
Main Results:
- Optimal transport is shown to solve key optimization problems in small system thermodynamics.
- Minimizing expected heat released or work done during finite-time nonequilibrium transitions is solved by the Burgers equation.
- Mass transport during these transitions is governed by the Burgers velocity field.
Conclusions:
- The study establishes a direct link between optimal transport and the thermodynamics of small systems.
- This work significantly broadens the scope of solvable optimization problems in nonequilibrium thermodynamics.
- Efficient numerical methods for optimal transport can now be applied to thermodynamic control challenges.
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