There is indeed a field of research that focuses on the thermal flow during quantum events. It is known as quantum thermodynamics. Quantum thermodynamics is an extension of classical thermodynamics that incorporates the principles of quantum mechanics.
In classical thermodynamics, the flow of heat and work between systems is described using macroscopic variables such as temperature, pressure, and energy. However, in the quantum realm, where individual particles or systems exhibit wave-particle duality and can be in superposition states, a more detailed and quantum mechanical description is required.
Quantum thermodynamics aims to provide a framework for analyzing and understanding the thermodynamic processes occurring at the quantum level. It deals with the transfer of heat, work, and energy in quantum systems and explores the connections between thermodynamic quantities such as entropy, temperature, and energy with quantum concepts like superposition, entanglement, and coherence.
In the context of your example, the formation of an ionic bond, quantum thermodynamics could be used to study the thermal flow and energy exchange that occurs during the bond formation process. It can provide insights into how the initial and final states of the system are connected, including the actual pathways followed during the transition.
Quantum thermodynamics offers tools and frameworks to investigate the thermodynamics of small-scale systems, such as individual molecules or nanoscale devices, where quantum effects become significant. It can be used to analyze processes involving quantum coherence, quantum fluctuations, and quantum heat engines, among other phenomena.
It's worth noting that the field of quantum thermodynamics is still an active area of research, and there are ongoing efforts to develop theoretical frameworks, experimental techniques, and practical applications. Researchers are exploring ways to describe and quantify thermodynamic processes at the quantum level, accounting for the unique features and challenges presented by quantum mechanics.