Physical Informatics

The physical roots, interpretation, controversies, and precise meaning of the Landauer principle are surveyed. The Landauer principle is a physical principle defining the lower theoretical limit of energy consumption necessary for computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat 2 per a bit of information to its surroundings. The Landauer principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit, and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin, and Bekenstein limits yields the minimal time of computation, which scales as t~h/kT. Decreasing the temperature of a thermal bath will decrease the energy consumption of a single computation, but in parallel, it will slow the computation. The Landauer principle bridges John Archibald Wheeler's "it from bit" paradigm and thermodynamics. Experimental verifications of the Landauer principle are surveyed. The interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to quantum and non-equilibrium systems is addressed. The Landauer principle represents the powerful heuristic principle bridging physics, information theory, and computer engineering.

The physical roots, interpretation, controversies and precise meaning of the Landauer Principle are surveyed. Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBlnT2 per a bit of information to its surrounding. The Landauer Principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin limit and Bekenstein limits yields the minimal time of computation, which scales as t~ℎ/KBT.. Decrease in a temperature of a thermal bath will decrease the energy consumption of a single computation, but, in parallel, it will slow the computation. The Landauer principle bridges between John Archibald Wheeler "it from bit" paradigm and thermodynamics. Experimental verifications of the Landauer Principle are surveyed. Interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to the quantum and non-equilibrium systems is addressed. Landauer Principle represents the powerful heuristic principle bridging the physics, information theory and computer engineering.

This talk addressed the following questions in the public debate at HoTPI: (i) energy dissipation limits of switches, memories and control; (ii) whether reversible computers are possible, or does their concept violate thermodynamics; (iii) Szilard’s engine, Maxwell’s demon and Landauer’s principle: corrections to their exposition in the literature; (iv) whether Landauer’s erasure– dissipation principle is valid, if the same energy dissipation holds for writing information, or if it is invalid; and (v) whether (non-secure) erasure of memories, or the writing of the same amount of information, dissipates most heat.

The frequent misunderstanding of information entropy is pointed out. It is shown that, contrary to fortuitous situations and common beliefs, there is no general interrelation between the information entropy and the thermodynamical entropy. We point out that the change of information entropy during measurement is determined by the resolution of the measurement instrument and these changes do not have a general and clear-cut interrelation with the change of thermal entropy. Moreover, these changes can be separated in space and time. We show classical physical considerations and examples to support this conclusion. Finally, we show that information entropy can violate the Third Law of Thermodynamics which is another indication of major differences from thermal entropy.

We prove that statistical information theoretic quantities, such as information entropy, cannot generally be interrelated with the lower limit of energy dissipation during information erasure. We also point out that, in deterministic and error-free computers, the information entropy of memories does not change during erasure because its value is always zero. On the other hand, for information-theoretic erasure-i.e., "thermalization" / randomization of the memory-the originally zero information entropy (with deterministic data in the memory) changes after erasure to its maximum value, 1 bit / memory bit, while the energy dissipation is still positive, even at parameters for which the thermodynamic entropy within the memory cell does not change. Information entropy does not convert to thermodynamic entropy and to the related energy dissipation; they are quantities of different physical nature. Possible specific observations (if any) indicating convertibility are at most fortuitous and due to the disregard of additional processes that are present.

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to- ...

In a recent article, Nature Communications 7 (2016) 12068, the authors claimed that they demonstrated sub-kBT energy dissipation at elementary logic operations. However, the argumentation is invalid because it neglects the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode, which totally dissipates during the full (0-1-0) cycle of logic values. The neglected dissipation phenomenon is identical with the mechanism that leads to the lower physical limit of dissipation (70-100 kBT) in today's microprocessors (CMOS logic) and in any other system with thermally activated errors thus the same limit holds for the new scheme, too. In a recent article [1], the authors claim that they demonstrate sub-k B T energy dissipation at elementary logic operations. In the experiments, they use Micro-Electromechanical Cantilevers (MEC) where the attractive electrostatic forces toward the input electrode(s) controlling the position of the cantilever tip. The Authors discuss an OR gate however, for the sake of simplicity but without the loss of generality, we investigate a Follower logic gate in this paper. Two separate tip positions define the two logic values, 0 and 1, respectively. These logic values and tip positions correspond to driving voltages 0 and U 1 on the input electrode. The energy dissipation (due to friction) in the cantilever is measured during changing the logic value and the Authors correctly conclude that the energy dissipation due to friction can be made smaller than k B T. This is the point where we must ask: Does this approach account for all the major energy loss phenomena determining the lower limit of energy dissipation or is there any dominant but neglected component? The answer is straightforward: The considerations in [1] neglected the energy dissipation due to charging and discharging the input capacitance, which are the same dissipation phenomena [2-6] that determine the lower limits of dissipation (70-100 k B T) [3] not only in today's microprocessors (CMOS logic) but also in any other system with thermally activated errors [2-4]. Thus the same dissipation limit (70-100 k B T) holds for the new scheme in [1], too.

This talk addressed the following questions in the public debate at HoTPI: (i) energy dissipation limits of switches, memories and control; (ii) whether reversible computers are possible, or does their concept violate thermodynamics; (iii) Szilard's engine, Maxwell's demon and Landauer's principle: corrections to their exposition in the literature; (iv) whether Landauer's erasuredissipation principle is valid, if the same energy dissipation holds for writing information, or if it is invalid; and (v) whether (non-secure) erasure of memories, or the writing of the same amount of information, dissipates most heat.

In 1961, Rolf Landauer argued that the erasure of information is a dissipative process 1 . A minimal quantity of heat, proportional to the thermal energy and called the Landauer bound, is necessarily produced when a classical bit of information is deleted. A direct consequence of this logically irreversible transformation is that the entropy of the environment increases by a finite amount. Despite its fundamental importance for information theory and computer science 2-5 , the erasure principle has not been verified experimentally so far, the main obstacle being the difficulty of doing single-particle experiments in the low-dissipation regime. Here we experimentally show the existence of the Landauer bound in a generic model of a one-bit memory. Using a system of a single colloidal particle trapped in a modulated double-well potential, we establish that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles. This result demonstrates the intimate link between information theory and thermodynamics. It further highlights the ultimate physical limit of irreversible computation.

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to-noise ratio. As a model system, a l/f-noise-driven Schmitt trigger has been investigated experimentally to study stochastic resonance with input 1/f noise. Under proper conditions, we have found several new nonlinearity effects, such as peaks at even harmonics, holes at even harmonics, and 1/f noise also in the output spectrum.

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to-noise ratio. As a model system, a l/f-noise-driven Schmitt trigger has been investigated experimentally to study stochastic resonance with input 1/f noise. Under proper conditions, we have found several new nonlinearity effects, such as peaks at even harmonics, holes at even harmonics, and 1/f noise also in the output spectrum.

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to-noise ratio. As a model system, a l/f-noise-driven Schmitt trigger has been investigated experimentally to study stochastic resonance with input 1/f noise. Under proper conditions, we have found several new nonlinearity effects, such as peaks at even harmonics, holes at even harmonics, and 1/f noise also in the output spectrum.