# White Noise Exemplifies the Constrained Disorder Principle-Based Concept of Overcoming Malfunctions
## 1 Introduction
### The Constrained Disorder Principle Accounts for All Types of Noise in the Universe  
The CDP describes systems according to their inherent noise, limited by dynamic boundaries that affect the noise level. It applies to all systems in the universe, characterizing them by their inherent variability. This variability is regulated by dynamic boundaries that continuously manage it, allowing for optimal adaptations to changes in both internal and external environments [1; 4; 5; 6]. Per the CDP, all biological systems exhibit a certain noise level crucial for proper functioning. This noise affects genes, cellular activities, and entire organs [4; 7; 8; 9; 10]. According to the CDP, malfunctions in these systems arise from dysfunctions at their boundaries, leading to either excessive or insufficient variability needed for optimal efficiency. This understanding allows for the development of second-generation artificial intelligence (AI) systems capable of regulating the degree of noise in complex systems to address and prevent malfunctions [21]. White Noise Is a Random Signal with Equal Intensity Across Different Frequencies, Resulting in a Constant Power Spectral Density  
White noise effectively demonstrates the CDP in the auditory system as a random signal. WN is a type of sound characterized by a uniform energy distribution across different frequency bands. It consists of all frequencies within the audible spectrum (20 Hz to 20,000 Hz) at equal intensity [22]. The spectral density of WN is flat, meaning its intensity remains constant across the human audible frequency range. Several vital characteristics define white Noise (WN): it has a continuous power spectral density across all frequencies, zero autocorrelation at any non-zero lag, and a flat frequency spectrum [23]. Additionally, it exhibits statistical independence between any two points in time. Its statistical features include a mean value typically zero, a probability distribution often Gaussian, and a constant and finite variance. When all the sounds a person can hear are combined, they create WN. Consequently, WN has unlimited bandwidth and a linear spectrum [24]. WN has several physical manifestations, including acoustic, electronic, and digital forms. Acoustic WN produces a consistent \"shhhh\" sound with equal energy across all frequency bands. Some tangible and straightforward examples of WN include the sounds of the sea crashing, rainfall, air conditioning units, fans, and static television [25; 26]. Electronic WN refers to thermal noise found in resistors and shot noise produced by electronic devices. This noise results from the random movement of electrons. Digital WN consists of computer-generated random sequences, including pseudo-random number generators, commonly used in digital signal processing. WN exists within a spectrum of noise colors [27; 28]. For example, Pink noise has decreasing intensity at higher frequencies; brown noise emphasizes lower frequencies, and blue noise shows increasing intensity at higher frequencies [29]. In discrete time, WN is a discrete signal made up of samples that create a sequence of serially uncorrelated random variables. Each of these variables has a mean of zero and a finite variance. A single instance of white noise can be regarded as a random shock. Furthermore, a random vector is classified as a WN vector or white random vector if each of its components has a probability distribution with a mean of zero, finite variance, and the components are statistically independent [30; 31]. The joint probability distribution of a vector must equal the product of the individual distributions of its components. Sometimes, the samples need to be independent and have identical probability distributions. Independent and identically distributed random variables represent the simplest form of WN. The signal is referred to as additive white Gaussian noise if each sample follows a normal distribution with a mean of zero [32].