# 2. Energy Flows A single registered distribution of energy, $$ u(\mathbf{r}), $$ says only how energy is distributed across the extent of $u$. If another registered distribution differs from it, we may label the two records $$ u_1(\mathbf{r}), \qquad u_2(\mathbf{r}). $$ Change is the acknowledgement of a difference between distributions. What is observed is not disappearance in one part of the extent of $u$ and reappearance in another, but continuous reconfiguration. Energy present in one part is registered in another. We interpret that observed reconfiguration as flow. To describe energy flow is to describe its continuous redistribution within itself. We write it as $$ \mathbf{S}(\mathbf{r};1,2). $$ The flow lines of $\mathbf{S}$ trace the reconfiguration by which $u_1$ becomes $u_2$. The energy field $u$ tells us how much energy is present. The flow $\mathbf{S}$ tells us how that energy redistributes.