A Dynamical Systems Perspective on the Thermodynamics of Late‐Time Cosmology

ABSTRACT A thermodynamic description of cosmological spacetimes may provide insights into the fundamentals of the cosmic evolution that remain otherwise obscure, similar to “black hole thermodynamics.” We investigate the thermodynamic properties of late‐time cosmological evolution using the dynamical systems approach, focusing on model and scalar field models with exponential potentials. Thermodynamic quantities obtained through the Hayward–Kodama formalism are mapped onto the phase‐space of these models. Specifically, we express the thermodynamic quantities as functions of the phase‐space variables, allowing us to study the thermodynamic behavior across the phase space, particularly at the critical points. We focus on thermodynamic stability and phase transitions, analyzed in an initial condition‐independent manner. In these models, the universe inevitably undergoes a thermodynamic phase transition, marked by diverging specific heats, irrespective of its initial configuration. We further demonstrate that the thermodynamic stability can occur only during an accelerating phase of the universe. For and quintessence models, the necessary stability conditions are never satisfied anywhere in the phase space, rendering both models thermodynamically unstable within the Hayward–Kodama framework and the canonical ensemble‐based stability criteria. Interestingly, the phantom models, although dynamically unstable, allow for the universe to attain thermodynamic stability in its asymptotic future. This can indicate the limitations of applying canonical ensemble‐based thermodynamic stability criteria to cosmological horizons. Through these archetypal descriptions of late‐time cosmology, we show that the dynamical system approach is a robust framework to probe the thermodynamic aspects of cosmological evolution.