  The extended Third Law of thermodynamics for nonequilibrium jump processes is
studied in previous collaborative papers (Kh et al.,2023) [1,2], where the
nonequilibrium heat capacity and the excess heat with the corresponding
quasipotential are introduced. The extended Third Law states that the
nonequilibrium heat capacity vanishes under two conditions as the temperature
approaches zero. The current paper presents a concise overview of key papers
addressing the nonequilibrium calorimetry and the nonequilibrium Nernst
postulate (the nonequilibrium Third Law of thermodynamics). The quasipotential
is a crucial quantity to calculate the nonequilibrium heat capacity. The new
result presented in this work includes an interpretation of the quasipotential
in terms of the mean time taken by the Markov jump process, starting from a
given state, to reach other states for the first time.
