Defining entropy bounds

Bekenstein's conjectured entropy bound for a system of linear size R and energy E, S ≤ 2πER, has counterexamples for many of the ways in which the 'system', R, E, and S may be defined. Here new ways are proposed to define these quantities for arbitrary nongravitational quantum field theories in flat spacetime, such as defining R as the smallest radius outside of which only vacuum expectation values occur. Difficulties of extending these definitions to gravitational quantum and semiclassical theories are noted.