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Thermodynamic limits of dynamic cooling.

Armen E Allahverdyan¹, Karen V Hovhannisyan, Dominik Janzing

¹Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

This study demonstrates that absolute zero temperature is unattainable for a driven two-level system, establishing a minimum reachable temperature. Minimal work cost for cooling decreases significantly as temperature rises above this minimum.

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Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation

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Area of Science:

Quantum thermodynamics
Statistical mechanics
Condensed matter physics

Background:

Dynamic cooling utilizes a reservoir to lower the temperature of a driven two-level system.
The third law of thermodynamics traditionally posits the unattainability of absolute zero.

Purpose of the Study:

To determine the minimum achievable temperature (T(min)) for a driven two-level system using dynamic cooling.
To analyze the work cost associated with reaching T(min) and explore methods for cost reduction.
To rigorously prove the unattainability of absolute zero temperature, resolving ambiguities in existing derivations.

Main Methods:

Investigating unitary dynamic processes acting on the system and reservoir.
Minimizing over all possible reservoir energy spectra.
Analyzing cooling with reservoirs of N identical spins and microcanonical states.

Main Results:

Explicitly derived a non-zero minimum temperature T(min) > 0 for the two-level system.
Established that the minimal work required grows as 1/T(min), with significant cost reduction for temperatures slightly above T(min).
Showed T(min) is inversely proportional to the number of spins (N) in a multi-spin reservoir.

Conclusions:

The findings provide an unambiguous proof for the unattainability of absolute zero.
Cooling via a large spin reservoir offers enhanced cooling efficiency (T(min) ∝ 1/N).
Imperfections in preparing microcanonical states reaffirm the unattainability of absolute zero.