Entropy production given constraints on the energy functions,Physical Review E

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Entropy production given constraints on the energy functions
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-23 , DOI: 10.1103/physreve.104.034129
Artemy Kolchinsky ₁ , David H Wolpert ₁

Affiliation

We consider the problem of driving a finite-state classical system from some initial distribution

p

to some final distribution

p^{'}

with vanishing entropy production (EP), under the constraint that the driving protocols can only use some limited set of energy functions

E

. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that such a transformation can be carried out, which is stated in terms of the smallest probabilities in

{p, p^{'}}

and a graph-theoretic property defined in terms of

E

. Our results imply that a surprisingly small amount of control over the energy function is sufficient (in particular, any transformation

p \to p^{'}

can be carried out as soon as one can control some one-dimensional parameter of the energy function, e.g., the energy of a single state). We also derive a lower bound on the EP under more general constraints on the transition rates, which is formulated in terms of a convex optimization problem.

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