Holography Defines Thermal Equilibrium in Strongly and Weakly Coupled Systems.

The behaviour of complex systems frequently involves interactions between components exhibiting vastly different characteristics, demanding novel approaches to understanding their collective dynamics. Recent research explores this phenomenon within the framework of semi-holography, a theoretical tool used to model gauge theories – fundamental theories describing forces and particles – by separating them into weakly and strongly interacting sectors. This allows physicists to investigate how these sectors, possessing distinct properties, evolve towards equilibrium when subjected to energy exchange. Toshali Mitra of the Institute for Theoretical Physics, University of Heidelberg, collaborates with Sukrut Mondkar from the Harish-Chandra Research Institute, Ayan Mukhopadhyay of the Instituto de Física, Pontificia Universidad Católica de Valparaíso, and Alexander Solovieve from the Faculty of Mathematics and Physics, University of Ljubljana, to address this challenge in their article, “Hybrid thermalization in the large limit”. Their work demonstrates that, under specific conditions, such a system relaxes towards a global equilibrium state, even when individual sectors exhibit differing temperatures, and provides a statistical analysis of this process.

Investigations into gauge theories currently employ semi-holography, a framework accommodating both perturbative and non-perturbative degrees of freedom. Physicists delineate these components using effective metrics and sources, while maintaining collective conservation of energy and momentum within a defined background metric. This approach facilitates modelling of complex systems, notably those encountered in high-energy heavy-ion collisions, where the formation of a quark-gluon plasma necessitates understanding strongly coupled quantum field theories. A gauge theory is a quantum field theory based on gauge symmetry, a type of symmetry where certain physical quantities remain unchanged under transformations.

Researchers establish a rigorous framework for understanding dynamics within gauge theories through the application of semi-holography. They separate interacting sectors, defining them by effective metrics and sources, while collectively conserving the total energy-momentum tensor within a shared physical background. This conservation is central to the model’s predictive power and allows for accurate simulations of complex systems. The energy-momentum tensor describes the density and flux of energy and momentum in spacetime.

The investigation confirms the existence and uniqueness of a global thermal equilibrium state, where both perturbative and non-perturbative sectors attain identical physical temperatures. Researchers identify this state as the configuration maximising entropy within the microcanonical ensemble, providing a firm foundation rooted in statistical mechanics. The microcanonical ensemble represents a collection of isolated systems with fixed energy, volume, and particle number. The proof of uniqueness solidifies the theoretical underpinnings of the semi-holographic approach and provides a powerful tool for analysing complex systems.

Furthermore, the research reveals that a typical non-equilibrium state of the isolated system relaxes towards this global equilibrium when the average energy density exceeds the scale dictated by the coupling between the two sectors. Researchers highlight the system’s tendency towards thermodynamic stability and provide a quantitative criterion for its attainment. The study therefore links initial conditions to eventual equilibrium states and allows for predictions about the system’s evolution.

The theoretical framework builds upon the AdS/CFT correspondence, a holographic duality relating gravitational theories in higher dimensions to quantum field theories in lower dimensions. By incorporating both perturbative and non-perturbative degrees of freedom, semi-holography offers a more nuanced approach to modelling strongly coupled systems, such as the quark-gluon plasma. The results contribute to a deeper understanding of thermalization mechanisms in extreme conditions and provide a statistical perspective on the evolution of isolated quantum systems.

Researchers confirm that a typical non-equilibrium state, representing the initial conditions following a heavy-ion collision, relaxes towards this global equilibrium when the average energy density surpasses the scale defined by the coupling between the two sectors. They utilize statistical mechanics to analyse this relaxation process, providing insights into the system’s evolution and the mechanisms driving thermalization. This finding suggests a natural tendency towards thermalization, a process where the system rapidly achieves a state of thermal equilibrium, even when starting from an initial non-equilibrium configuration.