发表机构
Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院费曼量子中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对温度编码计算的基础信息论极限，推导了有限容量热库的平均错误概率、信道容量与熵产生的边界，明确了热耗散与计算保真度的关系，为高能效模拟热力学硬件提供设计原则。
AI 中文摘要
自主量子热机近期被提出作为基于物理的计算基底，其中逻辑输入与输出编码于温度梯度。这类“热力学神经元”在计算保真度与热耗散间存在明确权衡，但温度编码计算的基础信息论极限仍未被表征。本文推导了远离平衡态运行的有限容量热库的平均错误概率、信道容量与熵产生间的严格边界，证明当平均错误概率〈ξ〉趋近于有限热库热涨落施加的基础最小错误下限εMin时，实现目标平均错误概率所需的最小耗散会发散；进一步建立了高耗散下饱和的热力学信道容量，并量化了级联网络维持目标保真度所需的最小耗散，证明其随网络深度存在O(L ln L)的基础开销，在强噪声放大条件下所需耗散增长至O(L³)。本文框架连接了随机热力学、有限时间信息论与自主计算，为高能效模拟热力学硬件提供了严格设计原则。
英文摘要
Autonomous quantum thermal machines have recently been proposed as physics-based computing substrates where logical inputs and outputs are encoded in temperature gradients. While such ``thermodynamic neurons'' exhibit a clear trade-off between computational fidelity and heat dissipation, the fundamental information-theoretic limits of temperature-encoded computation remain uncharacterized. Here, we derive rigorous bounds linking average error probability, channel capacity, and entropy production for finite-capacity thermal reservoirs operating far from equilibrium. We prove that the minimal dissipation required to achieve a target average error probability $\langle ξ\rangle$ diverges as $\langle ξ\rangle$ approaches a fundamental minimum error floor $\epsMin$ imposed by finite-reservoir thermal fluctuations. We further establish a thermodynamic channel capacity that saturates at high dissipation, and quantify the minimal dissipation required for cascaded networks to maintain target fidelity. We demonstrate that the required dissipation grows linearly $\mathcal{O}(L)$ with network depth for shallow networks, but diverges as the network depth $L$ approaches a fundamental maximum limit $L_{\max} = \epsNet/\epsMin$ imposed by the minimum error floor. Furthermore, under strong noise amplification conditions, the required dissipation can grow up to $\mathcal{O}(L^3)$. Our framework bridges stochastic thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient analog thermodynamic hardware.
Comments9 pages
