In this work we show the equivalence between Hamiltonian mechanics and conservation of information entropy. We will show that distributions with coordinate independent values for information entropy require that the manifold on which the distribution is defined is charted by conjugate pairs (i.e. it is a symplectic manifold). We will also show that further requiring that the information entropy is conserved during the evolution yields Hamilton's equations.

中文翻译：

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哈密​​顿力学是信息熵的守恒

在这项工作中，我们证明了哈密顿力学与信息熵守恒之间的等价性。我们将显示，信息熵具有与坐标无关的值的分布要求在其上定义分布的流形由共轭对绘制（即，它是一个辛流形）。我们还将表明，进一步要求在进化过程中信息熵必须守恒，从而产生汉密尔顿方程。