Abstract
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature. We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.
Highlights
Thermodynamics constitutes one of the basic foundations of modern science
All physical states reside in a region that is lower bounded by the horizontal axis (i.e. S = 0), corresponding to the pure states, and upper bounded by the convex curve (E(β), S(β)), which represents the thermal states of both positive and negative temperatures
The second law of thermodynamics is formulated in many different forms: as an upper bound on the extracted work, the impossibility of converting heat into work completely, etc
Summary
Thermodynamics constitutes one of the basic foundations of modern science. It plays an important role in modern technologies, but offers a basic understanding of a vast range of natural phenomena. By taking (i) global entropy preserving operations as the set of allowed operations and (ii) infinitely large thermal baths initially uncorrelated with the system, our formalism reproduces standard thermodynamics in its resource theoretic form. The resource theory of thermodynamics can be seen as one where condition (i) is sharpened, i.e. an extension of thermodynamics from coarse-grained to fine-grained information conservation, where the operations are global unitaries but still constrained to infinitely large thermal baths with a well defined temperature. The standard Helmholtz free energy singles out as the monotone that establishes the possible transitions between states, in contrast to the case of strict thermal operations, in which all the Rényi α-free energies are required This suggests that entropy preserving operations could be implemented with a single copy by means of a catalyst that can become correlated with the system.
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