Resource-resolved Quantum Fluctuation Theorems Enable Analysis of Nonequilibrium Systems

Understanding how energy fluctuates in systems far from equilibrium remains a central challenge in physics, and recent work by Sukrut Mondkar, Sayan Mondal, and Ujjwal Sen, all from the Harish-Chandra Research Institute, offers a significant advance in this area. The researchers developed a comprehensive framework for quantifying the influence of various physical resources, including heat, quantum coherence, and entanglement, on these fluctuations, moving beyond traditional approaches that often treat them as inseparable. By focusing on a measurement scheme that avoids initial energy determination, the team derives new fluctuation theorems and equalities that clearly separate the contributions of each resource, allowing for a detailed analysis of their individual effects. This achievement introduces novel concepts, such as the ‘weight of athermality’ and ‘fluctuation distances’, which provide operational measures of resource relevance and promise to deepen our understanding of nonequilibrium processes in diverse physical systems.

Quantum Thermodynamics and Fluctuation Theorem Foundations

This document presents a comprehensive overview of quantum thermodynamics, a field extending the laws of thermodynamics to the quantum realm. Unlike simply applying classical concepts, this field recognizes that quantum effects fundamentally alter how energy flows and work is performed. The work also explores fluctuation theorems, which describe the probabilities of deviations from classical thermodynamic laws, particularly the tendency for entropy to increase, and how these deviations become more pronounced in quantum systems. These theorems are crucial for understanding the limits of thermodynamic processes at the nanoscale.

Quantum coherence, where a system exists in multiple states simultaneously, plays a vital role in enhancing thermodynamic performance and enabling new types of quantum heat engines and refrigerators. The document explores how coherence affects work extraction, entropy production, and the validity of classical thermodynamic laws. Concepts from quantum information theory are used to quantify the resources available in quantum systems and understand their impact on thermodynamic processes. The research also considers non-Markovianity, where a system’s evolution depends on its entire past history, and how this affects thermodynamic behavior, leading to phenomena not observed in simpler systems.

The document delves into scenarios where classical thermodynamic assumptions break down, such as in the presence of initial correlations between system components, non-equilibrium environments, and strong quantum effects. It provides a detailed breakdown of foundational concepts like fluctuation theorems, the Kubo-Martin-Schwinger condition, quantum operations, and the impact of separability and entanglement. The work also examines key thermodynamic quantities, including work extraction, entropy production, heat exchange, and Landauer’s principle, which relates energy to information erasure. The research highlights that quantum thermodynamics is a rich and complex field, introducing new concepts and challenging our understanding of energy, work, and entropy.

Quantum coherence is a valuable resource that can be harnessed to enhance thermodynamic performance and enable new devices. Fluctuation theorems provide insights into nanoscale thermodynamics, helping us understand the limits of processes at this scale and the role of quantum fluctuations. Non-Markovian effects are important, as they can significantly alter thermodynamic behavior.

Athermal, Coherence, and Entanglement in Fluctuations

Scientists have developed a new framework for investigating quantum thermodynamics using the end-point measurement (EPM) scheme, a technique that avoids initial energy measurements to allow quantum resources to fully influence nonequilibrium statistics. This pioneering approach systematically derives fluctuation theorems, enabling researchers to isolate and quantify the roles of athermality, coherence, and entanglement in energy fluctuations. For single quantum systems, the team introduced the concept of the ‘weight of athermality’, a new measure quantifying the degree of non-thermalization, and combined it with the weight of coherence to separate classical uncertainty, athermality, and coherence contributions to fluctuations. This refined approach delivers fluctuation theorems that cleanly distinguish the effects of each resource on nonequilibrium energy statistics.

Extending the analysis to bipartite systems, scientists utilized a correlation-operator decomposition to capture total correlations, including entanglement, going beyond simple product structures. Furthermore, the study pioneers entanglement-resolved fluctuation theorems by combining the best separable approximation with local decompositions based on the weight of athermality and coherence. This combination delivers a family of theorems that quantify the contribution of entanglement to fluctuations. Beyond modified fluctuation relations, the team introduced new measures quantifying the thermodynamic relevance of coherence and entanglement, establishing a direct operational link between quantum resource theories and nonequilibrium thermodynamics. These measures capture the degree to which a given quantum resource affects nonequilibrium energy fluctuations, providing a powerful tool for understanding the interplay between quantum resources and thermodynamic behavior.

Athermal, Coherent, and Entangled Fluctuation Theorems Derived

This work presents a unified framework for understanding how quantum resources, specifically athermality, coherence, and entanglement, influence fluctuations in energy within non-equilibrium processes. Researchers developed fluctuation theorems that account for these quantum effects using the end-point measurement scheme, which avoids initial energy measurements and allows resources to impact energy statistics. The team successfully derived fluctuation theorems, including refined Jarzynski equalities and Crooks-type relations, where corrections cleanly separate contributions from each resource. For single quantum systems, scientists introduced the concept of the “weight of athermality” and combined it with the “weight of coherence” to isolate the distinct effects of these resources on fluctuations.

This allowed for a precise quantification of how each resource contributes to deviations from classical expectations. For bipartite systems, the research team obtained two families of entanglement-resolved fluctuation theorems, utilizing a correlation operator and the best separable approximation, providing tools to analyze the role of entanglement in energy fluctuations. Measurements confirm that the characteristic function takes a factorized form within the end-point measurement protocol, simplifying the analysis of how initial coherence and entanglement modify fluctuation relations. The team parameterized initial states to isolate the impact of coherence, deriving a Jarzynski equality that accounts for deviations arising from initial quantum coherence, quantified by the “coherence operator”.

This resulted in a refined equality where the deviation from unity directly reflects the influence of initial quantum coherence. Furthermore, the research establishes a Crooks-type detailed fluctuation theorem for entropy production, demonstrating how initial coherence affects the statistical properties of entropy fluctuations in the system. These results deliver a powerful toolkit for understanding and quantifying the thermodynamic roles of coherence, athermality, and entanglement in non-equilibrium quantum processes.

Quantum Resources Define Thermodynamic Fluctuations

This work presents a new framework for understanding fluctuations in energy and entropy, incorporating the influence of quantum resources such as athermality, coherence, and entanglement. Researchers developed fluctuation theorems that decompose corrections into contributions from these specific resources, moving beyond previous analyses that relied on less physically accessible decompositions of initial states. The approach utilizes experimentally preparable density matrices, ensuring all thermodynamic contributions are explicitly measurable. For both single and multiple particle systems, the team introduced methods to isolate the effects of athermality and coherence, and to disentangle classical and quantum correlations, including entanglement. This refined structure allows for a clear understanding of entropy production, identifying contributions from various sources. Furthermore, new measures, termed coherence and entanglement fluctuation distances, were defined as divergences that quantify how strongly these resources bias energy change statistics.