Abstract

This paper presents a novel theoretical framework and formal analysis demonstrating that non-Markovian quantum dynamics may prove to be an efficient model for a quantum thermodynamic description of the triple point, where solid, liquid, and gas phases coexist. To our knowledge, existing quantum-mechanical theories do not demonstrate a specific mechanism that clearly identifies how transient latent heat at the triple point can be precisely described at the quantum scale without ambiguity in the energy accounting required in order to be consistent with the first law of thermodynamics. We propose that at the triple point, critical fluctuations in the environment induce a sharp increase in the memory parameter gτB (product of system-bath coupling strength g and bath correlation time τB ), driving strongly non-Markovian behavior that invalidates conventional Markovian (Lindblad) master equations. We provide a formal demonstration that the transient latent heat observed at the triple point (a rapid increase in internal energy) maybe represented by energy temporarily residing in system-bath correlations. This non-Markovian approach inherently incorporates interaction energies without ambiguity, thereby satisfying the first law of thermodynamics without invoking the dynamical approximations typically present in Markovian master equations. We outline specific experimental approaches, including ultrafast spectroscopy and nanoscale thermometry, to detect the predicted non-Markovian signatures and provide empirical validation of this framework.