The ecosystem receives high-quality free energy and releases increasingly dispersed energy, principally as heat.
Therefore the corrected ecological principle is:
Matter cycles; usable free energy flows and dissipates.
Energy flow is directional through ecosystems, while biological elements are repeatedly recycled through biogeochemical systems. (OpenStax)
Operational definition
Governing ecosystem principle.
The one-way progression by which relatively concentrated, usable free-energy inputs enter living systems, undergo successive transformations and transfers, and become increasingly dispersed in lower-capacity forms, principally environmental heat.
This does not mean energy is destroyed. It means:
total energy is conserved
while:
capacity to perform useful work declines
Thus the authoritative ecological formulation is:
matter cycles; usable free energy flows and dissipates
Gross production, respiration, net production, trophic transfer, and ecosystem respiration quantify successive parts of this system-level flow. (OpenStax)