Year: 2026
Type: preprint
Abstract: Quantum thermodynamics is traditionally formulated as a theory of equilibrium states and state transformations. Recent advances in higher-order quantum transformations, which describe physical scenarios beyond states and channels and provide a systematic framework for causal order, raise the question of how equilibrium should be defined and preserved in this more general setting. Starting from the Gibbs state as the unique equilibrium state, we identify equilibrium preservation as its natural higher-order extension. We show that, while this principle can in general give rise to distinct classes of transformations, all such distinctions disappear when equilibrium preservation is required completely, namely under arbitrary ancillary extensions. Remarkably, every transformation satisfying this condition is causally ordered, making causal order an emergent consequence of thermodynamic equilibrium. We establish this result for arbitrary higher-order maps and use the resulting framework to introduce free-energy-like quantities for quantum channels. Our findings reveal a fundamental connection between thermodynamic equilibrium and causal structure, providing a foundation for a fully fledged theory of higher-order quantum thermodynamics.
Source: arXiv (Cornell University)
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: Slovenská Akadémia Vied, Innovation, Science and Economic Development Canada, Government of Canada, European Commission, Austrian Science Fund, Ministry of Science and Technology of the People's Republic of China, Agentúra na Podporu Výskumu a Vývoja, Vedecká Grantová Agentúra MŠVVaŠ SR a SAV, Institut Périmètre de physique théorique, HORIZON EUROPE Framework Programme, CAS Key Laboratory of Quantum Information
OpenAlex ID: W7213305299
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