Statistical Thermodynamics of Small Open Quantum Systems: Grounding the Relative Energy Window Entropy in Non-Hermitian Quantum Mechanics
Faculty: Prof. Ananth Govind Rajan (CE) and Prof. Awadhesh Narayan (SSSCU)
Statistical mechanics is an important field of physics and physical chemistry that allows one to describe the thermodynamic properties of a system from a first-principles lens. For isolated systems (i.e., in the microcanonical ensemble), there has been a longstanding debate on the use of Gibbs’ volume entropy versus Boltzmann’s surface entropy. In this regard, the relative energy window (REW) entropy, recently proposed to resolve the century-old Gibbs-Boltzmann inconsistency in microcanonical statistical mechanics, replaces the fixed energy tolerance of conventional approaches with a window that scales with the system’s excess energy above its ground state. This construction was originally motivated by a heuristic argument based on the Heisenberg energy-time uncertainty principle. However, no isolated system is ever perfectly closed, as real small systems, such as nanoclusters, trapped ions or water molecules, and molecular junctions, are always weakly coupled to a continuum of environmental states. In this regard, non-Hermitian quantum mechanics provides the natural, first-principles language for describing such situations. This project will derive the REW energy window directly from the system’s linewidth in realistic open-system models, replacing the current ansatz with a first-principles, system-specific energy window, and testing whether this resolves thermodynamic inconsistencies for various model Hamiltonians. The project will also involve applying the REW formalism to realistic nanoscale materials systems via molecular dynamics simulations. This will allow checking the applicability of REW entropy to practical systems, such as two-dimensional materials and nanoconfined water. Overall, the project sits at the interface of statistical mechanics, open-quantum-systems theory, and nanoscale materials physics, and offers a concrete path toward placing REW entropy on a rigorous microscopic foundation rather than a phenomenological one.