PHY.3:4.3 - Construct a comparison that exposes the restriction

Choose the operation that fits the available physical structure. The following two constructions address different situations and can be used independently.

Compose with a reference and cancel selected changes. Use this when an admitted reference process exchanges the relevant quantities or restores a needed condition. Choose the part of the proposal you want to eliminate from the combined account, then determine the reference’s direction, amount and preparation that match it. Establish that the reference can perform that operation under the same connecting conditions. For example, two processes may exchange equal energy but require incompatible temperatures, pressures, phases or forms of delivery. Numerical equality alone cannot establish the physical connection.

Combine the proposed and reference operations, including their auxiliaries. Cancel only the matched exchanges or restored states; keep all remaining changes. C.29.BB supplies the accounting for additive quantities. Apply the physical restriction to the composite. If it would have a prohibited net effect, derive the inequality or condition on the original proposal that avoids that effect. A reference may be an ideal process admitted by the theory; building it in a laboratory is unnecessary for this conditional argument. Using the inverse in an equation still requires a reason that the needed physical reverse process is admitted.

Compare inputs of the same operation. Use this when one device must perform the requested transformation on a family of inputs and a physical law relates its actions on different inputs. Select inputs whose relation can expose the limitation. Write their proposed outputs, including allowed auxiliary outputs, while holding fixed the device and its input-independent preparation. Derive the relation the law requires between those outputs. If the requested outputs violate it, the common device cannot provide them under the stated conditions.

An auxiliary output may depend on the input even when the initial preparation cannot. Allow that dependence in the comparison. Requiring the auxiliary to return to a fixed state when the proposal permits a changed state would prove a narrower restriction. Conversely, choosing a different apparatus separately for each input would answer a different question from the fixed-device requirement.

These constructions can reveal a remaining physical premise rather than a bound. Name that premise and what supplying it would enable. Forcing either comparison when its connection conditions or input relation are absent adds no physical result.