Quantifying Memory Capacity as a Quantum Thermodynamic Resource

Area of Science:

• Quantum thermodynamics
• Information theory
• Statistical mechanics

Background:

• Memory acts as a thermodynamic resource, enabling heat-to-work conversion.
• Szilard's engine model demonstrates this link using a simple two-state memory.
• Generalizing this concept to complex quantum systems requires a new formalism.

Purpose of the Study:

• To develop a method for quantifying the thermodynamic value of memory in general quantum systems.
• To introduce and define the 'thermal information capacity' for quantum memory.
• To investigate the relationship between thermal information capacity and established thermodynamic quantities like free energy.

Main Methods:

• Devised a formalism to quantify the thermodynamic value of memory in general quantum systems.
• Analyzed systems with nontrivial energy landscapes.
• Computed the capacity exactly for a two-state (qubit) memory system away from the thermodynamic limit.
• Investigated the convergence of thermal information capacity to nonequilibrium Helmholtz free energy in the thermodynamic limit.

Main Results:

• The thermal information capacity quantifies the thermodynamic value of quantum memory.
• In the thermodynamic limit, thermal information capacity converges to the nonequilibrium Helmholtz free energy.
• For a general two-state (qubit) memory, the computed capacity differs from known free energies.
• An explicit memory-bath coupling was proposed to approximate the optimal qubit thermal information capacity.

Conclusions:

• The thermal information capacity provides a robust measure for the thermodynamic utility of quantum memory.
• This capacity exhibits distinct behavior from traditional free energies, particularly for finite quantum systems like qubits.
• The findings offer a pathway to experimentally realizing and utilizing the thermodynamic value of quantum information.