[Paper Review] Out of equilibrium thermodynamics of quantum harmonic chains

Andrew Carlisle, Laura Mazzola+8 more|Arrow@dit (Dublin Institute of Technology)|Mar 3, 2014

Advanced Thermodynamics and Statistical Mechanics1 references3 citations

TL;DR

This paper investigates the out-of-equilibrium thermodynamics of one-dimensional quantum harmonic chains subjected to a sudden quench in inter-oscillator coupling, using an interferometric approach to analytically compute the work distribution and fluctuation relations. It reveals a direct functional link between dissipated work and quantum correlations in a two-oscillator chain, demonstrating that non-classical features significantly influence thermodynamic behavior in quantum many-body systems.

ABSTRACT

The thermodynamic implications for the out-of-equilibrium dynamics of quantum systems are to date largely unexplored, especially for quantum many-body systems. In this paper we investigate the paradigmatic case of an array of nearest-neighbor coupled quantum harmonic oscillators interacting with a thermal bath and subjected to a quench of the inter-oscillator coupling strength. We study the work done on the system and its irreversible counterpart, and characterize analytically the fluctuation relations of the ensuing out-of-equilibrium dynamics. Finally, we showcase an interesting functional link between the dissipated work produced across a two-element chain and their degree of general quantum correlations. Our results suggest that, for the specific model at hand, the non-classical features of a harmonic system can influence significantly its thermodynamics.

Motivation & Objective

• To understand the thermodynamic behavior of quantum many-body systems under non-equilibrium conditions, particularly focusing on work, free energy changes, and irreversibility.
• To address the lack of analytical frameworks for composite quantum harmonic systems beyond single-oscillator models.
• To characterize the scaling of thermodynamic quantities—especially dissipated work—with system size in coupled harmonic chains.
• To explore the interplay between quantum correlations and thermodynamic irreversibility in a minimal two-oscillator model.
• To establish a rigorous quantum mechanical framework for work and fluctuation theorems in non-adiabatic, quenched quantum systems.

Proposed method

• Formulates the Hamiltonian of an N-oscillator chain with nearest-neighbor harmonic coupling and coupling to a thermal bath.
• Applies a global quench to the inter-oscillator coupling strength, inducing non-equilibrium dynamics.
• Uses an interferometric decomposition to map the quench evolution to a sequence of beam-splitting and phase-rotation operations.
• Employs the characteristic function of the work distribution via coherent state evolution and displacement-squeezing transformations.
• Derives exact analytical expressions for average work, free energy change, and dissipated work using the transformation laws of quadrature operators.
• Relies on the matrix $ P $ and its entries to determine the effective transformation of mode quadratures, enabling exact computation of the work characteristic function.

Experimental results

Research questions

• RQ1 How does the dissipated work scale with system size in a quenched quantum harmonic chain?
• RQ2 What is the functional relationship between quantum correlations and thermodynamic irreversibility in a two-oscillator system?
• RQ3 Can quantum fluctuation theorems be exactly computed for extended quantum harmonic systems under global quenches?
• RQ4 How do quantum correlations—such as squeezing and entanglement—manifest in thermodynamic quantities like work and free energy differences?
• RQ5 What is the role of non-adiabaticity in determining the deviation from equilibrium thermodynamics in many-body quantum systems?

Key findings

• The paper derives exact analytical expressions for the average work, free energy change, and dissipated work in a quenched N-oscillator harmonic chain.
• It identifies a clear functional relationship between the dissipated work and the degree of quantum correlations in a two-oscillator chain, indicating that non-classical features directly influence thermodynamic irreversibility.
• The interferometric approach enables exact computation of the work characteristic function by transforming the quench dynamics into a sequence of beam-splitting and phase-rotation operations.
• The method allows for the separation of classical and quantum contributions to the free energy change, with the quantum part linked to squeezing and correlations.
• The results show that the degree of squeezing generated by quadratic coupling acts as a key resource for work extraction, even in non-adiabatic processes.
• The framework is general and applicable to chains of arbitrary length, providing a foundation for studying scaling laws and non-equilibrium thermodynamics in quantum many-body systems.