Energy, Causality, and Coherence

Patrick Suppes, Mario Zanotti

Hai Li, Hsien-Chen Ma, Yaming Hao +1 more

In recent years, quantum battery (QB) models have emerged as crucial platforms for exploring the connections between quantum effects and energy within the framework of quantum thermodynamics. Inspired by the physical implementation of quantum switch (QS), we, in this work, present a simple QB model in which a two-level system as battery, under a series of coherent chargers, performs the indefinite causal order (ICO) charging by introducing a control qubit as QS. Within the energy-preserving collision interaction framework, we analyze the charging ICO and conventional definite causal order (DCO) dynamics, respectively, and discover the underlying connection between the final charged states of battery in ICO and DCO charging modes. That is, the ICO charged state can be understood as a split of the DCO charged state, accompanied by an offset caused by the interference component characterizing the ICO effect. That provides direct theoretical evidence that the ICO effect positively influences the ergotropy (i.e., the maximum extractable work) of QB only when quantum coherence is present in the charging process, and it is independent of the average stored energy of the QB. By combining numerical simulations, we examine that quantum coherence in our model is a strong quantum resource contributing to the ergotropy of QB, while the ICO effect plays a catalyst-like role, assisting quantum coherence in further enhancing the ergotropy of the battery. In addition, we also demonstrate that increasing the number of chargers also benefits the optimal ergotropy of QB. Finally, we reveal that, when the coherent chargers are subject to the dephasing channel, the ICO charging mode is more robust against dephasing noise than the DCO charging mode. This investigation deepens our understanding of quantum coherence and the ICO effect in the context of quantum thermodynamics.

Jiaxuan Yang

We derive a universal upper bound on the temperature of macroscopic quantum coherence, based on information causality and quantum speed limits. The bound, \( T_c \leq \frac{\hbar}{2k_B} \cdot \frac{v_{\text{LR}}}{\xi_0} \), arises from the interplay between the Lieb-Robinson information speed and the energy-time uncertainty principle. Without any fitting parameters, it accurately predicts the superfluid transition temperature of $^4$He (2.185 K vs. experimental 2.172 K) when geometric effects are included. The bound applies across diverse systems—from superconductors to black holes—suggesting a fundamental connection between quantum coherence, causality, and information propagation. This work highlights information causality as a foundational constraint on macroscopic quantum phenomena. The manuscript has been submitted to Physical Review Letters.

Peter J. Riggs

Časlav Brukner

Osvaldo Frota Pessoa Junior

This paper is the first step in an investigation of whether microscopic events can be reduced to a mereological composition of elementary events, especially in biological systems. The hypothesis is made that, between events in which quanta are exchanged, there is causal flow, but strictly speaking no events take place. A causal event is characterized by the possibility of an intervention or manipulation. Thus, three types of quantum mechanical events may be found: (1) detection of a quantum of energy; (2) confinement by an apparatus in a Glauber coherent state; (3) null result measurement (without exchange of quanta). The paper explores these three types of elementary causal events, e sets forth as the next step the investigation of the causal events involved in the action of a molecular motor.