Ecosystems process energy and matter in fundamentally different ways.

Energy enters most ecosystems as sunlight, is converted into chemical energy by primary producers, passes through consumers and decomposers, and is progressively transformed into less usable thermal energy during metabolism.

Thus energy flow is directional:

$$\text{external energy input} \rightarrow \text{biological chemical energy} \rightarrow \text{heat}. $$

Matter behaves differently. Carbon, nitrogen, phosphorus, water and other materials are rearranged chemically and transferred among organisms, atmosphere, water, soil and rocks, but their atoms are not consumed as energy is dissipated.

Matter therefore cycles among reservoirs:

$$\text{environment} \rightleftarrows \text{organisms} \rightleftarrows \text{environment}. $$

This distinction explains why ecosystems require a continuing energy input but can reuse the same chemical elements repeatedly.

For example, a carbon atom can move from atmospheric $CO_2$ into a plant, then into an herbivore, then return to the atmosphere through respiration. The energy captured during photosynthesis does not make the same closed loop: some of it is eventually released as heat at every metabolic step.

The key principle is

$$\boxed{\text{energy flows; matter cycles}.}$$

Biogeochemical cycles describe the matter side of this distinction, while trophic energetics describe the energy side.