Higher-order quantum thermodynamics: equilibrium and causal structure
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.
Related
- de Sitter Spacetime: Geometry, Causal Structure, and Quantum Fields
- Quantum field theory with scale-dependent weighted measures: nonlinear momentum representations, vacuum fluctuations, and causal structure
- Quantum Metrology for Signals with an Unknown Causal Structure
- The Structure of Higher-Order Quantum Resources with an Application to Coherence
- Analysis, thermodynamics, and a numerical solver for a pressure-temperature equilibrium closure of the four-equation model
BibTeX
@misc{milz2026higherorder,
title = {{Higher-order quantum thermodynamics: equilibrium and causal structure}},
author = {Simon Milz and Kyrylo Simonov and Zoltán Zimborás and Tamal Guha and Saptarshi Roy and Giulio Chiribella},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15829},
eprint = {2609.15829},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15829},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Higher-order quantum thermodynamics: equilibrium and causal structure
AU - Simon Milz
AU - Kyrylo Simonov
AU - Zoltán Zimborás
AU - Tamal Guha
AU - Saptarshi Roy
AU - Giulio Chiribella
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15829
UR - https://arxiv.org/abs/2609.15829
AB - 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.
ER -