Finite-time thermodynamic bounds and tradeoff relations for information processing

• Main Authors: Kamijima, Takuya, Funo, Ken, Sagawa, Takahiro
• Format: Journal Article
• Language: English
• Published: 13-09-2024
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2409.08606

In thermal environments, information processing requires thermodynamic costs
determined by the second law of thermodynamics. Information processing within
finite time is particularly important, since fast information processing has
practical significance but is inevitably accompanied by additional dissipation.
In this paper, we reveal the fundamental thermodynamic costs and the tradeoff
relations between incompatible information processing such as measurement and
feedback in the finite-time regime. To this end, we introduce a general
framework based on the concept of the Pareto front for thermodynamic costs,
revealing the existence of fundamental tradeoff relations between them.
Focusing on discrete Markov jump processes, we consider the tradeoff relation
between thermodynamic activities, which in turn determines the tradeoff
relation between entropy productions. To identify the Pareto fronts, we
introduce a new Wasserstein distance that captures the thermodynamic costs of
subsystems, providing a geometrical perspective on their structure. Our
framework enables us to find the optimal entropy production of subsystems and
the optimal time evolution to realize it. In an illustrative example, we find
that even in situations where naive optimization of total dissipation cannot
realize the function of Maxwell's demon, reduction of the dissipation in the
feedback system according to the tradeoff relation enables the realization of
the demon. We also show that an optimal Maxwell's demon can be implemented by
using double quantum dots. Furthermore, our framework is applicable to larger
scale systems with multiple states, as demonstrated by a model of chemotaxis.
Our results would serve as a designing principle of efficient thermodynamic
machines performing information processing, from single electron devices to
biochemical signal transduction.