Classical harmonic oscillators are ubiquitous mechanical systems, appearing in many setups, in particular, as Gauss–Markov processes. The connection between wave motion and harmonic oscillators leads us to a connection between waves and a special class of infinitely dimensional Gauss–Markov processes.

It is the aim of this work to explore this connection in the simplest case, namely, that of a linear wave on a string with fixed end points. We shall see that the initial conditions are unknown and distributed according to a Gaussian measure, the string is an infinite dimensional Gaussian Markov process.

A byproduct of the setup, is that the logarithm of the characteristic function of a Gaussian wave is a concave function ( it is the negative) of the Fenchel–Lagrange dual of the energy, that could perhaps be thought of as the “entropy” of the solution to the wave equation.

经典的谐波振荡器是无处不在的机械系统，在许多情况下都会出现，特别是在高斯-马尔可夫过程中。波动与谐波振荡器之间的联系将我们引向了波动与一类特殊的无限维高斯-马尔可夫过程之间的联系。

这项工作的目的是在最简单的情况下探索这种连接，即具有固定端点的弦上的线性波的连接。我们将看到初始条件是未知的，并且根据高斯测度分布，字符串是无限维的高斯马尔可夫过程。

该设置的一个副产品是，高斯波特征函数的对数是能量的Fenchel-Lagrange对偶的凹函数（它是负数），可以将其视为能量的“熵”。波动方程的解。