This question invites researchers from different fields—quantum physics and thermodynamics—to explore interdisciplinary connections. By bridging two seemingly unrelated domains, it encourages discussions on novel applications of quantum phenomena to classical systems. This could lead to groundbreaking insights and experimental proposals, attracting a wide audience keen on exploring the frontiers of physics.
I dont expect that much from that combination , perhaps missing something.
Not sure I quite understand the question, so please bear with me if I misunderstand - there is no such thing as 'principles' of quantum entanglement, there is only a quite precise mathematical definition of what entanglement is (in a nutshell, two or more entities are entangled if the variables representing them are the co-variables of a function Ψ satisfying a valid Schrödinger equation. Since, incidentally, distance does not appear in the formalism, it plays no role).
This being said, trying to make use of entanglement for practical , actionable purposes is fraught with major issues.
For instance, you cannot transmit information via entanglement : if, say, two particles at points A and B are entangled, a potential receiver of information (at point B) has no possible way of determining whether something he sees, such as a change of state in B, is due to information indeed transferred from a change to the particle in A, or to a change of state caused by some other interference in A (which may come from a quantum random change), or even to a random event in B, without anything actually having happened in A. All attempts to work around those limitations fail.
As for classical problems in thermodynamics, I'm not sure which problems are outstanding? We do understand entropy, statistical themrodynamics, its child the kinetic theory of gases, etc. rather well.