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Inclusive Thermodynamics of Computational Machines

G\"ulce Karde\c{s}David Wolpert
Jun 2022
摘要
We introduce a framework to analyze the thermodynamics of a physical systemthat first implements an abstractly defined computational machine and then isreinitialized, completing a full thermodynamic cycle. Our starting point is toderive a lower bound on the dissipated work that occurs in a complete cycle ofany classical or quantum physical process that implements a given computationalmachine. It turns out that this lower bound on dissipated work exactly equalsthe expected entropy production arising in the Hamiltonian formulation ofstochastic thermodynamics. This leads us to derive an integral fluctuationtheorem for the dissipated work of any system modeled using the Hamiltonianformulation, along with a mismatch cost theorem. Explicitly connecting ourframework with computer science, we analyze how the lower bound on dissipatedwork depends on the size complexity of a deterministic finite automaton. Weprove that given a set of equivalent automata, the one with minimal sizecomplexity is the one with minimal dissipation. This result is valid for alldeterministic finite automata and at all iterations. We also provide a modifiedversion of the exchange fluctuation theorem for computational machines. Inaddition to considering a deterministic finite automaton, we present resultsconcerning the thermodynamics of a Markov information source (i.e., a hiddenMarkov model), and those concerning the possible use of rate distortion theoryin Shannon communication channels.
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