Work and heat exchanged during sudden quenches of strongly coupled quantum systems (2502.19418v1)

Abstract: How should one define thermodynamic quantities (internal energy, work, heat, etc.) for quantum systems coupled to their environments strongly? We examine three (classically equivalent) definitions of a quantum system's internal energy under strong-coupling conditions. Each internal-energy definition implies a definition of work and a definition of heat. Our study focuses on quenches, common processes in which the Hamiltonian changes abruptly. In these processes, the first law of thermodynamics holds for each set of definitions by construction. However, we prove that only two sets obey the second law. We illustrate our findings using a simple spin model. Our results guide studies of thermodynamic quantities in strongly coupled quantum systems.

Thermodynamics of Strongly Coupled Quantum Systems: Analysis of Sudden Quenches

The exploration of thermodynamic properties in quantum systems that strongly couple with their environments represents a pivotal topic in quantum thermodynamics. The paper conducted by Davoudi et al. explores identifying suitable definitions for thermodynamic quantities like internal energy, work, and heat for such quantum systems. The investigation centers on processes characterized by sudden changes in the system's Hamiltonian, known as quenches.

Key Contributions

The paper primarily examines three distinct definitions of internal energy relevant for strongly coupled quantum systems:

1. $U_{diff}$ - This definition considers the internal energy as the total system-reservoir energy minus the reservoir's equilibrium energy.
2. $U_{H^*}$ - This approach utilizes the Hamiltonian of mean force, a construct emerging from averaging out reservoir degrees of freedom.
3. $U_{E^*}$ - Based on the derivative of the product of the inverse temperature and the Hamiltonian of mean force, this definition accounts for temperature effects explicitly.

The authors scrutinize these definitions with respect to compliance with the laws of thermodynamics, particularly the first and second laws. The analysis is carried out using quantum quench processes, where change is abrupt, providing a clear distinction between work (energy change due to the Hamiltonian shift) and heat (energy exchange due to system-reservoir interaction).

Results and Conclusions

A significant conclusion from the paper is that, while all three internal energy definitions naturally satisfy the first law of thermodynamics, only $U_{diff}$ and $U_{H^*}$ align with the second law under the specific quench conditions analyzed. The choice of $U_{E^*}$ could lead to inconsistencies with the second law, evidenced by potential violations during the quantitative analyses, especially using spin systems as models.

The computations and derivations are encapsulated in two primary quench scenarios: system quench, affecting the system Hamiltonian, and interaction quench, impacting the interaction between the system and reservoir. Notably, when interaction terms commute, all definitions of work return equivalent values, suggesting conceptual similarity in such specific circumstances.

Implications and Future Directions

This paper sheds light on foundational questions in quantum thermodynamics, especially in delineating work and heat in quantum systems where traditional weak-coupling approximations fail. The framework and results aid in advancing robust theoretical underpinnings required for understanding thermal and energetic properties in advanced quantum technologies and materials, including quantum simulations and lattice gauge theories.

Future research is directed at extending these definitions to fluctuating thermodynamic quantities within strongly coupled regimes, potentially unearthing new fluctuation relations analogous to classical stochastic thermodynamics. This extension could enrich the theoretical landscape of quantum entropy production, cooling mechanisms, and engine efficiencies in quantum thermal machines.

Furthermore, the work inspires novel experimental strategies for direct access to these thermodynamic quantities via state tomography and related techniques, bridging the gap between theoretical predictions and experimental validations in the quantum field.

In conclusion, this detailed exploration offers critical insights into the thermodynamic behavior of strongly coupled quantum systems and outlines pathways for theoretical and experimental advancements in quantum thermodynamics.