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Fig. 1.
Physical abstraction of an information processing artifact, such as a QCA
circuit, and its surroundings in a globally closed universe.
of the subsystems that are coupled in each step, allows determination of the fun-
damental lower bounds that we are after in this work.
Process Abstraction:
During computation the subsystems are driven away from
equilibrium but then rethermalized as a part of the process abstraction. We iden-
tify a set of local physical operations
φ
t
∗{φ
t
}
, each of which is decomposed into
a control process and a restoration process. Control operations are the local oper-
ations that act during specified time intervals to change the states of representa-
tional elements in the artifact either unconditionally or conditioned on the states
of other representational elements. Typically, they involve interaction between
the artifact, other information-bearing subsystems, and the bath. Restoration
processes are the local operations that couple the remote environment
¯
B
to the
bath
. These operations rethermalize the bath
and recharge the reservoirs after they have been driven from their nominal states
by control operations. Together, the control and restoration phases make up the
sequence of global system evolutions required for implementation of computation
in the circuit.
B
and local particle reservoirs in
A
Analysis.
The second step in our approach involves spacetime decomposition
of the circuit function (operational decomposition) and physical-information-
theoretic analyses of local dissipation into the bath throughout the computa-
tional cycle (cost analysis). Any local information about the initial state of
A
that is irreversibly lost during a computational step induces dissipation in
B
¯
before being swept completely into
during the restoration process. Note that,
loss of initial-state information from part of
B
is locally irreversible if it is erased
in the absence of interaction with other parts of
A
¯
that hold or receive
copies of the initial state during the clock step. This locally irreversible infor-
mation loss affects the state of
A
or
A
during an operation's control process, which
is precisely the point at which the dissipation costs are “cashed out” in our
approach. The manual calculation of our bounds involves calculation of dissipa-
tion for each step of and summing the contribution to obtain the total cost of
the complete computation cycle. The details of this procedure is outlined below.
B
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