Heat Conduction and Finite Measures for Transition Times between Steady States

A finite time, the mean action time associated with the conductivetransition from a constant initial temperature to thermal equilibriumat a constant ambient temperature, is related to time lag constants,mean energy residence times, mean first passage times, and Green'sfunction properties for linear equations, and to freezing timesand finite transition times for problems with phase transitions.When the boundary conditions are linear of mixed type and theconductivity is constant, or when they are of Dirichlet typeand the conductivity perhaps temperature dependent, the meanaction time is given by the solution of a linear Poisson problem.It is then easily found and is a useful finite comparative timefor the thermal transition process, giving a measure of itsdependence on size and other geometric factors.