AdS/CFT Duality Provides a Holographic Framework for Work Distribution and Fluctuation Theorems

Understanding how energy changes in complex systems remains a fundamental challenge in physics, and recent work by Daichi Takeda from iTHEMS, RIKEN, and colleagues explores this question using a powerful theoretical framework. The researchers derive a new connection between systems described by the AdS/CFT correspondence and the distribution of work performed within those systems, effectively creating a way to study energy fluctuations in a holographic model. This achievement yields a bulk formulation of the Tasaki-Crooks fluctuation theorem, offering a novel approach to investigate energy transfer and potentially revealing insights into “mesoscopic” phenomena, which bridge the gap between microscopic and macroscopic behaviours. The team’s work establishes a holographic prescription for understanding work distributions, opening new avenues for exploring energy dynamics in complex systems through the lens of gravity and quantum field theory.

Researchers derived a bulk formulation of the work distribution by examining measurements on the boundary of the system, effectively creating a holographic prescription for understanding how work fluctuates, and bridging the gap between microscopic and macroscopic scales. The team constructed a model using a specific background field configuration and solved for field perturbations, adhering to stringent boundary conditions. This involved constructing a manifold from both Euclidean and Lorentzian black hole spacetimes, ensuring smoothness and consistency, and finding a solution for the scalar field in Fourier space, normalized to behave as an outgoing mode near the horizon. Through detailed calculations involving the action and its boundary terms, the researchers arrived at a precise expression for a generated quantity, confirming the validity of the approach and providing a concrete link between the holographic description and the actual work performed in the system. This opens new avenues for studying energy dissipation and fluctuation theorems in complex systems.

Work Distribution Encodes Holographic Gravity Dynamics

This research establishes a connection between work distributions in boundary conformal field theories and gravitational dynamics in their holographic duals, utilising the AdS/CFT correspondence to formulate a bulk description of the Tasaki-Crooks fluctuation theorem. By expressing the work distribution in terms of bulk quantities, the team demonstrated agreement between calculations of average work derived from the boundary theory and those obtained from metric perturbations in the bulk, suggesting that the work distribution encodes information about gravitational dynamics and implying a potential link between fluctuation theorems in quantum field theory and corresponding theorems governing aspects of gravity. While this study focused on single-trace deformations and scalar primary operators, the authors acknowledge that extending the theorem to multi-trace deformations, charged or spinning operators, and higher orders in the perturbation parameter represents a natural progression. Future research directions include exploring the relationship between this newly derived fluctuation theorem and existing results, as well as applying it to composite holographic conformal field theories and open or composite systems with gravity, ultimately aiming to precisely formulate the bulk dual of the trajectory probability measure and connect the work distribution to the underlying bulk quantum process.

Holography, Thermodynamics and Fluctuation Theorems

Classical gravity emerges naturally from thermodynamic principles, suggesting a deep connection between gravity and the microscopic structure of the universe. Quantities like mass, angular momentum, and area in black holes obey a first law, where area plays a role similar to entropy, and this connection is reinforced by the area-increase theorem, analogous to the second law of thermodynamics, and corroborated by calculations of microstates in string theory. The Einstein equation itself can be interpreted as a local expression of this first law, suggesting that gravity arises from underlying thermodynamic principles. This research area explores the interplay between holography, quantum thermodynamics, fluctuation theorems, and related concepts.

A central theme is the AdS/CFT correspondence, which proposes a duality between gravitational theories in Anti-de Sitter space and conformal field theories on its boundary, serving as a powerful tool for studying strongly coupled quantum systems. A significant portion of the research focuses on applying thermodynamic concepts, such as work, heat, and free energy, to quantum systems far from equilibrium, including fluctuation theorems, which describe the probabilities of rare events in nonequilibrium systems. Fluctuation theorems, like the Jarzynski equality and the Crooks fluctuation theorem, are central to understanding the statistical behavior of systems driven out of equilibrium, relating the work done on a system to the probability of observing specific trajectories. Researchers are increasingly studying open quantum systems, those interacting with an environment, as these interactions lead to dissipation and decoherence, crucial for realistic physical models, using the Schwinger-Keldysh formalism to describe the real-time evolution of quantum systems in nonequilibrium situations, and noting the connection to black hole physics, as black holes are inherently thermodynamic objects.

Research in this area can be broadly categorized into foundational work exploring the AdS/CFT correspondence and holographic reconstruction, studies focusing on quantum thermodynamics and fluctuation theorems, both in general and specifically within the context of AdS/CFT, and investigations of open quantum systems and dissipation in holography, often using double-trace deformations to model these effects. Counting statistics and fluctuation theorems are also being applied to quantum fields, evolving from studying equilibrium properties to understanding how systems behave when driven out of equilibrium, with AdS/CFT providing a powerful way to study strongly coupled quantum systems where traditional methods fail. A major challenge is incorporating dissipation and decoherence into holographic models, addressed using double-trace deformations and open quantum system techniques. There is a growing emphasis on understanding the real-time evolution of quantum systems, crucial for describing physical processes, with the Schwinger-Keldysh formalism becoming increasingly important for studying nonequilibrium dynamics. Current efforts focus on developing more realistic holographic models of open quantum systems, understanding the connection between holography and quantum information, and exploring the implications of double-trace deformations.