The second law of thermodynamics, which asserts the non-negativity of theaverage total entropy production of a combined system and its environment, is adirect consequence of applying Jensen's inequality to a fluctuation relation.It is also possible, through this inequality, to determine an upper bound ofthe average total entropy production based on the entropies along the mostextreme stochastic trajectories. In this work, we construct an upper boundinequality of the average of a convex function over a domain whose average isknown. When applied to the various fluctuation relations, the upper bounds ofthe average total entropy production are established. Finally, by employing theresult of Neri, Rold\'an, and J\"ulicher [Phys. Rev. X 7, 011019 (2017)], weare able to show that the average total entropy production is bounded only bythe total entropy production supremum, and vice versa, for a generalnon-equilibrium stationary system.
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机译：热力学第二定律断言一个组合系统及其环境的平均总熵产生是非负的，这是将詹森不等式应用于波动关系的直接结果，也可以通过这种不等式确定一个上限基于沿最极端随机轨迹的熵的平均总熵产生的界限。在这项工作中，我们构造了一个凸函数的平均值在一个已知平均值的域上的上界质量。当将其应用于各种波动关系时，建立了平均总熵产生的上限。最后，通过使用Neri，Rold \'an和J \“ ulicher [Phys。Rev. X 7，011019（2017）]的结果，穿戴者能够证明平均总熵产仅受总熵产至上的限制。 ，反之亦然，对于一般的非平衡固定系统。
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