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Adiabatic Processes for an Ideal Gas

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When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...

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Shortcuts to Adiabaticity across a Separatrix.

Roi Holtzman¹, Oren Raz¹, Christopher Jarzynski²

¹Weizmann Institute of Science, Department of Physics of Complex Systems, Rehovot, 76100, Israel.

Physical Review Letters

|May 2, 2025

Summary

Researchers developed Hamiltonian shortcuts to adiabaticity to cross phase-space separatrices, enabling energy shell transitions. This method allows for efficient erasure procedures with consistent fidelity and energy cost, regardless of protocol duration.

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Area of Science:

Quantum mechanics
Classical mechanics
Statistical mechanics

Background:

Adiabatic invariants are conserved under slow driving conditions.
Shortcuts to adiabaticity (STA) extend this conservation to fast-driving regimes.
Crossing a phase-space separatrix is typically not possible with adiabatic protocols.

Purpose of the Study:

To extend classical Hamiltonian shortcuts to adiabaticity.
To enable the crossing of phase-space separatrices.
To design a protocol-independent erasure procedure.

Main Methods:

Construction of a time-dependent Hamiltonian.
Evolving systems across a phase-space separatrix.
Designing an erasure procedure based on the new Hamiltonian.

Main Results:

Successfully extended Hamiltonian STA to cross separatrices.
Demonstrated evolution between energy shells across a separatrix.
Developed an erasure procedure with protocol-duration-independent energy cost and fidelity.

Conclusions:

Hamiltonian STA can be generalized to non-adiabatic scenarios involving separatrices.
This approach offers a new method for state manipulation and erasure in physical systems.
The developed erasure procedure provides robust performance irrespective of the driving speed.