In this talk, we are briefly surveying our recent results [1-3] about two very popular yet often misunderstood concepts in physical informatics: (i) The existence of Johnson noise at near to absolute zero temperature has been debated many times yet it is generally accepted [1]. We point out the fundamental problems [2] with the particular approach the related quantum theories [4] of Fluctuation-Dissipation Theorem are using. Then we prove that the existence of zero-point noise would allow the construction of a perpetual motion machine [1]. Finally, we cite early works pointing out that the observed “zeropoint” noise in experiments [7] with phase-sensitive linear amplifiers is an amplifier-noise [5,6] due to the uncertainty principle, and it does not exist in the resistor in an objective way, independently from the measurement [1,2]. Thus a correct derivation of the Fluctuation-Dissipation Theorem must include [1] the type of experimental setup used for the measurement. (ii) The general opinion is that information entropy and thermal entropy are interchangeable. This belief triggered Brillouin's negentropy principle of information [8], and Landauer's claimed principle [9] about energy dissipation during information erasure that has been debated on many occasions [10-19]. Here we show the newest and perhaps the simplest arguments [3] proving that the two types of entropies are apples and oranges and are not interchangeable.
In this talk, we are briefly surveying our recent results [1-3] about two very popular yet often misunderstood concepts in physical informatics: (i) The existence of Johnson noise at near to absolute zero temperature has been debated many times yet it is generally accepted [1]. We point out the fundamental problems [2] with the particular approach the related quantum theories [4] of Fluctuation-Dissipation Theorem are using. Then we prove that the existence of zero-point noise would allow the construction of a perpetual motion machine [1]. Finally, we cite early works pointing out that the observed “zeropoint” noise in experiments [7] with phase-sensitive linear amplifiers is an amplifier-noise [5,6] due to the uncertainty principle, and it does not exist in the resistor in an objective way, independently from the measurement [1,2]. Thus a correct derivation of the Fluctuation-Dissipation Theorem must include [1] the type of experimental setup used for the measurement. (ii) The general opinion is that information entropy and thermal entropy are interchangeable. This belief triggered Brillouin's negentropy principle of information [8], and Landauer's claimed principle [9] about energy dissipation during information erasure that has been debated on many occasions [10-19]. Here we show the newest and perhaps the simplest arguments [3] proving that the two types of entropies are apples and oranges and are not interchangeable.
Abstract There is a longstanding debate about the zero-point term in the Johnson noise voltage of a resistor. This term originates from a quantum-theoretical treatment of the fluctuation-dissipation theorem (FDT). Is the zero-point term really there, or is it only an experimental artifact, due to the uncertainty principle, for phase-sensitive amplifiers? Could it be removed by renormalization of theories? We discuss some historical measurement schemes that do not lead to the effect predicted by the FDT, and we analyse new features that emerge when the consequences of the zero-point term are measured via the mean energy and force in a capacitor shunting the resistor. If these measurements verify the existence of a zero-point term in the noise, then two types of perpetual motion machines can be constructed. Further investigation with the same approach shows that, in the quantum limit, the Johnson–Nyquist formula is also invalid under general conditions even though it is valid for a resistor-antenna system. Therefore we conclude that in a satisfactory quantum theory of the Johnson noise, the FDT must, as a minimum, include also the measurement system used to evaluate the observed quantities. Issues concerning the zero-point term may also have implications for phenomena in advanced nanotechnology.
The bandwidth of transistors in logic devices approaches the quantum limit, where Johnson noise and associated error rates are supposed to be strongly enhanced. However, the related theory — asserting a temperature-independent quantum zero-point (ZP) contribution to Johnson noise, which dominates the quantum regime — is controversial and resolution of the controversy is essential to determine the real error rate and fundamental energy dissipation limits of logic gates in the quantum limit. The Callen–Welton formula (fluctuation–dissipation theorem) of voltage and current noise for a resistance is the sum of Nyquist’s classical Johnson noise equation and a quantum ZP term with a power density spectrum proportional to frequency and independent of temperature. The classical Johnson–Nyquist formula vanishes at the approach of zero temperature, but the quantum ZP term still predicts non-zero noise voltage and current. Here, we show that this noise cannot be reconciled with the Fermi–Dirac distribution, which defines the thermodynamics of electrons according to quantum-statistical physics. Consequently, Johnson noise must be nil at zero temperature, and non-zero noise found for certain experimental arrangements may be a measurement artifact, such as the one mentioned in Kleen’s uncertainty relation argument.
The Callen-Welton formula (fluctuation-dissipation theorem) of voltage and current noise of a resistance are the sum of Nyquist's classical Johnson noise equations and a (quantum) zero-point term with power density spectrum proportional to frequency and independent of temperature. At zero temperature, the classical Nyquist term vanishes however the zero-point term produces non-zero noise voltage and current. We show that the claim of zero-point noise directly contradicts to the Fermi-Dirac distribution, which defines the thermodynamics of electrons according to quantum-statistical physics. As a consequence, the Johnson noise must be zero at zero temperature, which is in accordance with Nyquist's original formula. Further investigation shows that the Callen-Welton derivation has conceptual errors such as neglecting phonon scattering, disregarding the Pauli principle during calculating the transition probabilities and using bosonic (linear oscillator) energies leading to the zero-point noise artifact. Following Kleen's proposal, the possible origin of the heterodyne (Koch - van Harlingen - Clark) experimental results are also discussed in terms of Heffner theory of quantum noise of frequency/phase-sensitive linear amplifiers. Experiments that failed to see the zero-point noise term are also mentioned.
While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution. Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.
An ensemble of spins oriented along the z direction exhibits nonzero fluctuation in the transverse (x- and y-) components of the spin angular momentum in accordance with the uncertainty principle. When the spins obey a spin temperature distribution, the mean square fluctuation in Sx can be calculated by ensemble average of the expectation value of Sx2 with respect to an equilibrium density matrix ρ=eβSz/Z. The fluctuation can also be calculated from the fluctuation-dissipation theorem as has been done in literature in the context of NMR spin noise. For spin 1/2 particles in the high temperature limit, appropriate for many NMR experiments, the two methods are known to produce the same, temperature-independent spin noise. We show that inclusion of the zero-point fluctuation term in the original Nyquist relation extends this correspondence to an arbitrary spin temperature for any spin S. This indicates that the uncertainty principle-limited spin projection noise can be viewed as a result of the zero-point fluctuation in the thermal bath coupled to the spins.
Recently, it has been shown that excess noises generated or modified by chemical agents can be used to detect and identify chemicals with enhanced sensitivity and selectivity. Moreover thermal noise and its artificial versions (Johnson‐like noises) can be utilized as information carriers with peculiar properties. The first application is called Fluctuation‐Enhanced Sensing. The second class can be called Thermal Noise Informatics with relevant topics are Zero Power Classical Communication and (in the quantum limit) Zero‐Quantum Quantum Communication; Thermal Noise Driven Computing; and Totally Secure Classical Communication. In the paper version of this talk, we will briefly describe the scope of these fields and in the oral talk we also provide extended considerations and results.