Irreversible entropy production, from quantum to classical (2009.07668v4)

Abstract: Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium processes. It is also often used in attempts to provide the quantitative characterization of logical and thermodynamic irreversibility, stemming from processes in physics, chemistry and biology. Notwithstanding its fundamental character, a unifying theory of entropy production valid for general processes, both classical and quantum, has not yet been formulated. Developments pivoting around the frameworks of stochastic thermodynamics, open quantum systems, and quantum information theory have led to substantial progress in such endeavour. This has culminated in the unlocking of a new generation of experiments able to address stochastic thermodynamic processes and the impact of entropy production on them. This paper aims to provide a compendium on the current framework for the description, assessment and manipulation of entropy production. We present both formal aspects of its formulation and the implications stemming from the potential quantum nature of a given process, including a detailed survey of recent experiments.

• The paper develops a unified framework for irreversible entropy production, bridging quantum and classical thermodynamics using principles from stochastic thermodynamics and quantum information theory.
• It explores the transition from quantum to classical dynamics, analyzing how quantum features like coherence and correlations influence thermodynamic behavior and how the classical limit emerges.
• The framework enhances understanding of non-equilibrium processes and offers practical insights for optimizing efficiency and managing entropy production in emerging quantum technologies.

Irreversible Entropy Production, from Quantum to Classical

The paper by Gabriel T. Landi and Mauro Paternostro provides a comprehensive exploration of entropy production in thermodynamic processes, encompassing both quantum and classical systems. Entropy production is a cornerstone of non-equilibrium thermodynamics, intimately linked to the second law, which postulates that entropy generation is non-negative and zero only for reversible processes. Despite its importance, a unified theoretical framework covering general processes, regardless of their quantum or classical nature, has been elusive. This work presents advancements towards such a framework, grounded in recent developments in stochastic thermodynamics, open quantum systems, and quantum information theory.

Key Frameworks and Insights

• Entropy Production Foundations: Central to any finite-time thermodynamic process, entropy production, denoted by $\Sigma$, satisfies $\Sigma \geq 0$. This paper works towards a unified description of entropy production by considering the global unitary dynamics of a system plus its environment, embracing quantum unitary evolutions and information-theoretic considerations. By doing so, it ties together classical thermodynamic interpretations with quantum information-theoretic measures such as mutual information and relative entropy.
• Quantum to Classical Transition: The authors delve into how quantum features affect classical thermodynamic paradigms. They explore how the classical limit emerges from quantum dynamics, notably focusing on the role of coherence and correlations, which are pivotal in quantum regimes but diminish in classical ones. This transition is vital for understanding macroscopic classical systems' behaviors based on quantum mechanical principles.
• Resource Theory and Thermodynamics: Another significant aspect of this work is its application to resource theories, particularly the resource theory of athermality. Here, a state’s deviation from thermal equilibrium is seen as a resource that can be quantified and manipulated. Thermal operations, key in this context, help reformulate the second law in terms of generalized information-theoretic quantities, providing a broader lens through which to view thermodynamic transitions and transformations.

Implications and Future Directions

• Enhanced Understanding of Non-Equilibrium Phenomena: By unifying quantum and classical views, this framework enhances our understanding of non-equilibrium processes, crucial for technological applications such as quantum computing and information systems where thermal management and entropy production are critical.
• Practical Applications in Quantum Technologies: Insights from this work could drive advances in optimizing quantum technologies, where the balance of coherent quantum operations and associated entropy production will be vital for operational efficiency and fidelity.
• Pathways for Future Research: Future research may focus on fully integrating this framework with experimental platforms, examining non-classical thermodynamic cycles in quantum systems or leveraging the interplay of coherence and thermodynamics for enhanced energy efficiency in nanoscale engines.

In summary, this paper bridges important concepts from classical and quantum thermodynamics and provides a robust framework to understand and quantify entropy production across these domains. This not only deepens theoretical understanding but also sets the stage for novel applications in emerging quantum technologies.