[Paper Review] Information and Entropy in Quantum Brownian Motion : Thermodynamic Entropy versus von Neumann Entropy ()

Christian Hörhammer, H. Büttner|arXiv (Cornell University)|Dec 2, 2008

Advanced Thermodynamics and Statistical Mechanics36 references36 citations

TL;DR

This paper compares thermodynamic entropy from the subsystem's partition function with von Neumann entropy from its reduced density matrix in a quantum Brownian oscillator. It finds significant deviations at low temperatures due to entanglement between the particle and environment, highlighting implications for information-thermodynamics principles like Landauer's principle.

ABSTRACT

We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two entropies which are due to the fact that the Brownian particle and its environment are entangled. We give an explanation for these findings and point out that these deviations become important in cases where statements about the information capacity of the subsystem are associated with thermodynamic properties, as it is the case for the Landauer principle.

Motivation & Objective

• To investigate the relationship between thermodynamic entropy derived from the partition function and von Neumann entropy from the reduced density matrix in a quantum Brownian oscillator.
• To identify the origin of discrepancies between these two entropy measures in quantum open systems.
• To assess the physical significance of these deviations, particularly in contexts involving information capacity and thermodynamic constraints.
• To clarify the role of entanglement between the subsystem and environment in altering entropy interpretations.
• To evaluate the relevance of these findings for foundational principles such as Landauer's principle in quantum information thermodynamics.

Proposed method

• Derives the thermodynamic entropy of the quantum Brownian oscillator using the partition function of the subsystem.
• Computes the von Neumann entropy from the reduced density matrix of the Brownian particle after tracing out the environment.
• Analyzes the system in the low-temperature regime to highlight deviations between the two entropy measures.
• Identifies entanglement between the Brownian particle and its environment as the source of entropy discrepancies.
• Uses statistical mechanics and quantum statistical mechanics formalism to compare entropy definitions in open quantum systems.
• Applies the framework to assess implications for information-theoretic principles such as Landauer's principle.

Experimental results

Research questions

• RQ1 How do thermodynamic entropy and von Neumann entropy compare in a quantum Brownian oscillator at low temperatures?
• RQ2 What physical mechanism causes deviations between thermodynamic and von Neumann entropy in open quantum systems?
• RQ3 To what extent does entanglement between the subsystem and environment affect entropy interpretations?
• RQ4 How do these entropy discrepancies impact the validity or interpretation of Landauer's principle?
• RQ5 In what scenarios do these differences become physically significant for information capacity and thermodynamic constraints?

Key findings

• Significant deviations between thermodynamic entropy and von Neumann entropy emerge at low temperatures in the quantum Brownian oscillator.
• These deviations are attributed to quantum entanglement between the Brownian particle and its environment.
• The entanglement prevents the subsystem from being described by a pure state, invalidating direct equivalence between the two entropy measures.
• The discrepancy becomes physically relevant when linking information capacity to thermodynamic properties.
• The findings underscore the limitations of using von Neumann entropy alone to describe thermodynamic behavior in entangled open quantum systems.
• The results support the need for careful interpretation of entropy in quantum information thermodynamics, especially in the context of Landauer's principle.