AI 中文总结
该研究针对可逆连续时间马尔可夫网络，推导了误差与熵产生率、记忆时间的不等式，确立了随机网络信息处理的热力学极限，为理解生物计算的能量成本提供定量框架。
AI 中文摘要
生物和人工网络通过将随时间变化的输入转化为功能性输出来进行计算。由于随机网络的内部状态会在有限时间尺度上弛豫，其输出通常滞后于变化的环境，从而产生计算误差。我们证明，对于可逆连续时间马尔可夫网络，该误差存在一个普适的热力学界。将总误差分解为表征误差和滞后误差两部分，我们推导了一个不等式，将滞后误差与熵产生率以及等于输出可观测量积分平衡自相关的记忆时间关联起来。该界表明，精确的动态计算要么需要大量耗散，要么需要编码在缓慢弛豫模式中的长寿命记忆。我们在人工马尔可夫网络和生化信息处理模型中验证了这些原理。我们的结果确立了随机网络中信息处理的热力学极限，并为理解生物计算的能量成本提供了定量框架。
英文摘要
Biological and artificial networks compute by transforming time-dependent inputs into functional outputs. Because the internal state of a stochastic network relaxes on finite timescales, its output generally lags behind a changing environment, producing computational errors. We show that for reversible continuous-time Markov networks the error admits a universal thermodynamic bound. Decomposing the total error into representation and lag contributions, we derive an inequality relating the lag error to the entropy production rate and a memory time equal to the integrated equilibrium autocorrelation of the output observable. The bound implies that accurate dynamical computation requires either substantial dissipation or long-lived memory encoded in slowly relaxing modes. We demonstrate these principles in artificial Markov networks and in models of biochemical information processing. Our results establish a thermodynamic limit on information processing in stochastic networks and provide a quantitative framework for understanding the energetic costs of biological computation.
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