Beyond the classical theory of heat conduction: a perspective view of future from entropy.

Energy is conserved by the first law of thermodynamics; its quality degrades constantly due to entropy generation, by the second law of thermodynamics. It is thus important to examine the entropy generation regarding the way to reduce its magnitude and the limit of entropy generation as time tends to infinity regarding whether it is bounded or not. This work initiates such an analysis with one-dimensional heat conduction. The work not only offers some fundamental insights of universe and its future, but also builds up the relation between the second law of thermodynamics and mathematical inequalities via developing the latter of either new or classical nature. A concise review of entropy is also included for the interest of performing the analysis in this work and the similar analysis for other processes in the future.