Ray Kyle J, Boyd Alexander B, Guarnieri Giacomo, Crutchfield James P
Complexity Sciences Center and Department of Physics and Astronomy, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.
Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev E. 2023 Nov;108(5-1):054126. doi: 10.1103/PhysRevE.108.054126.
Thermodynamic uncertainty relations (TURs) express a fundamental lower bound on the precision (inverse scaled variance) of any thermodynamic charge-e.g., work or heat-by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend TUR inequalities by incorporating and analyzing the impact of higher statistical cumulants of the entropy production itself within the general framework of time-symmetrically-controlled computation. We derive an exact expression for the charge that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name the thermodynamic uncertainty theorem (TUT). Importantly, both the minimum scaled variance charge and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any charge's precision. This is made explicit via a thorough numerical analysis of "swap" and "reset" computations that quantitatively compares the TUT against previous generalized TURs.
热力学不确定性关系（TURs）通过平均熵产生的泛函，表达了任何热力学量（如功或热）的精度（逆标度方差）的基本下限。依靠纯粹的变分论证，我们通过在时间对称控制计算的一般框架内纳入并分析熵产生本身的高阶统计累积量的影响，显著扩展了TUR不等式。我们推导出了实现最小标度方差的量的精确表达式，对于该表达式，TUR界限收紧为一个等式，我们将其命名为热力学不确定性定理（TUT）。重要的是，最小标度方差量和TUT都是随机熵产生的泛函，从而保留了其高阶矩的影响。特别是，我们的结果表明，除了平均值之外，熵产生分布的高阶矩对任何量的精度都有显著影响。这通过对“交换”和“重置”计算的全面数值分析得以明确，该分析定量地将TUT与先前的广义TURs进行了比较。
