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The second laws of quantum thermodynamics
Fernando Brandão1, Michał Horodecki2, Nelly Ng3
1Department of Computer Science, University College London, London WC1E 6BT, United Kingdom;
Summary
The second law of thermodynamics has new constraints for microscopic systems. Generalized free energies, which never increase, reveal a family of laws governing state transitions in small systems.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Quantum Information Theory
Background:
- The second law of thermodynamics traditionally applies to macroscopic systems.
- Exploring thermodynamic laws for microscopic systems interacting with a heat bath is an active research area.
- Understanding these laws is crucial for advancements in quantum technologies and nanoscale devices.
Purpose of the Study:
- To investigate the validity and form of the second law of thermodynamics in the microscopic regime.
- To identify new constraints on state transformations for small systems.
- To unify the laws of thermodynamics within a single theoretical framework.
Main Methods:
- Formulation of generalized free energies that generalize the traditional free energy.
- Analysis of state transformations under approximately cyclic processes.
- Identification of three distinct regimes governing thermodynamic transitions based on process cyclicity.
Main Results:
- The second law for microscopic systems imposes a family of constraints, not just one.
- A family of generalized free energies is introduced, all of which are non-increasing.
- Apparent violations of the usual second law can occur in specific regimes through work embezzlement.
- The framework unifies thermodynamic laws, with the first law defining operations and the zeroth law defining thermal state equivalence.
Conclusions:
- The generalized second laws are relevant for both small systems and individual macroscopic systems with long-range interactions.
- The monotonicity of generalized free energies provides additional constraints on thermodynamic transitions.
- This work offers a unified perspective on the laws of thermodynamics, applicable across different scales.
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