The Autocorrelation And Spectrum Characteristic Of Thermal Noise In Water

It is the dream for human being to design and produce the molecular machine which can achieve a specific function.Researchers have been constantly made effort to make this dream come true.Recent years,theoretical workers have designed several nano pumps which can transport uni-directionally water molecules.These pumps bring infinite imagination in the desalination.The physical mechanism behinds these nano pumps may be interpreted by the molecular ratchet,in which contains two necessary conditions,i.e.,the appropriate asymmetric system and colored noise.Hence,whether thermal noise in water is colored or white is of fundamental importance in understanding the pumps.In the traditional theory,there is not biased transportation in the system with spatial asymmetry without any external input,since thermal noise is regarded as white.Based on molecular dynamics(MD)simulations,our simulation results show that thermal noise has an autocorrelation time length of ~10 ps in water at room temperature,this fact indicates that thermal noise is not white in the molecular scale while thermal noise can be reasonably assumed as white in macro-and meso-scale systems.Our simulation results also show that the autocorrelation time length of thermal noise is independent of different methods of thermostats and different coupling parameters of thermostats,it depends on the reference temperature of system.Thus,the finite autocorrelation time of thermal noise in water is intrinsic.Remarkably,the hydrogen bonds had similar autocorrelation behavior as thermal noise in MD simulations.The correlation time of thermal noise and the lifetime of hydrogen bond show similar trends as the change of temperature.Since hydrogen bond is the main interaction between water molecule and neighboring water molecules,this suggests that the finite autocorrelation time length of thermal noise is associated with the finite lifetime of the interactions between neighboring water molecules.Since thermal noise is not white in the molecular scale and power spectrum analysis can distinguish the detail colors of thermal noise in each frequency domain,we used the power spectrum to analyze the thermal noise on different solutes(polar and non-polar solutes)from surrounding solvent water molecules.The results from spectral analysis show that the thermal noise of solute molecules in water is non-white on the molecular scale,which is in contrast to conventional theory.For polar and non-polar solute molecules,the power spectrum of thermal noise resembles the spectrum of white noise in the low-frequency domain,and is close to the spectrum of red noise when the frequency is greater than 5×1013 Hz.Interestingly,in the intermediate frequency domain(from 2×1011 Hz to 1013 Hz),the power spectrum of thermal noise for polar solute molecules resembles the spectrum of 1/? noise.The power spectrum of thermal noise for non-polar solute molecules only deviates slightly from the spectrum of white noise.This can be attributed to the formation of hydrogen bonds between polar solute molecules and solvent water molecules,while there are no hydrogen bonds between the non-polar solute and solvent molecules.Moreover,for polar solute molecules,the degree of power spectrum departure from that of white noise is associated with the average lifetime of hydrogen bonds between the solute and the solvent molecules.This finding,thermal noise has an intrinsic autocorrelation time length of ~10 ps,has important significance in understanding many unidirectional movement in the asymmetric systems at nanoscale.Moreover,because living organisms are mainly composed of polar molecules(such as water)that are rich in hydrogen bonds,our finding that the thermal noise spectrum for polar molecules resembles the spectrum of 1/? noise in the intermediate-frequency domain may provide a perspective of the molecular composition for understanding the ubiquity of 1/? noise in living organisms.