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Register a new userDynamical randomness, information, and Landauers principle
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New concepts from nonequilibrium thermodynamics are used to show that Landauers principle can be understood in terms of time asymmetry in the dynamical randomness generated by the physical process of the erasure of digital information. In this way, Landauers principle is generalized, showing that the dissipation associated with the erasure of a sequence of bits produces entropy at the rate $k_{{rm B}}I$ per erased bit, where $I$ is Shannons information per bit.
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We present an experiment in which a one-bit memory is constructed, using a system of a single colloidal particle trapped in a modulated double-well potential. We measure the amount of heat dissipated to erase a bit and we establish that in the limit of long erasure cycles the mean dissipated heat saturates at the Landauer bound, i.e. the minimal quantity of heat necessarily produced to delete a classical bit of information. This result demonstrates the intimate link between information theory and thermodynamics. To stress this connection we also show that a detailed Jarzynski equality is verified, retrieving the Landauers bound independently of the work done on the system. The experimental details are presented and the experimental errors carefully discussed
Almost sixty years since Landauer linked the erasure of information with an increase of entropy, his famous erasure principle and byproducts like reversible computing are still subjected to debates in the scientific community. In this work we use the Liouville theorem to establish three different types of the relation between manipulation of information by a logical gate and the change of its physical entropy, corresponding to three types of the final state of environment. A time-reversible relation can be established when the final states of environment corresponding to different logical inputs are macroscopically distinguishable, showing a path to reversible computation and erasure of data with no entropy cost. A weak relation, giving the entropy change of $k ln 2$ for an erasure gate, can be deduced without any thermodynamical argument, only requiring the final states of environment to be macroscopically indistinguishable. The common strong relation that links entropy cost to heat requires the final states of environment to be in a thermal equilibrium. We argue in this work that much of the misunderstanding around the Landauers erasure principle stems from not properly distinguishing the limits and applicability of these three different relations. Due to new technological advances, we emphasize the importance of taking into account the time-reversible and weak types of relation to link the information manipulation and entropy cost in erasure gates beyond the considerations of environments in thermodynamic equilibrium.
We study Landauers Principle for Repeated Interaction Systems (RIS) consisting of a reference quantum system $mathcal{S}$ in contact with a structured environment $mathcal{E}$ made of a chain of independent quantum probes; $mathcal{S}$ interacts with each probe, for a fixed duration, in sequence. We first adapt Landauers lower bound, which relates the energy variation of the environment $mathcal{E}$ to a decrease of entropy of the system $mathcal{S}$ during the evolution, to the peculiar discrete time dynamics of RIS. Then we consider RIS with a structured environment $mathcal{E}$ displaying small variations of order $T^{-1}$ between the successive probes encountered by $mathcal{S}$, after $nsimeq T$ interactions, in keeping with adiabatic scaling. We establish a discrete time non-unitary adiabatic theorem to approximate the reduced dynamics of $mathcal{S}$ in this regime, in order to tackle the adiabatic limit of Landauers bound. We find that saturation of Landauers bound is equivalent to a detailed balance condition on the repeated interaction system, reflecting the non-equilibrium nature of the repeated interaction system dynamics. This is to be contrasted with the generic saturation of Landauers bound known to hold for continuous time evolution of an open quantum system interacting with a single thermal reservoir in the adiabatic regime.
The clean world of digital information is based on noisy physical devices. Landauers principle provides a deep connection between information processing and the underlying thermodynamics by setting a lower limit on the energy consumption and heat production of logically irreversible transformations. While Landauers original formulation assumes equilibrium, real devices often do operate far from equilibrium. We show experimentally that the nonequilibrium character of a memory state enables full erasure with reduced power consumption as well as negative heat production. We implement the optimized erasure protocols in an optomechanical two-state memory. To this end, we introduce dynamical shaping of nonlinear potential landscapes as a powerful tool for levitodynamics as well as the investigation of far-from-equilibrium processes.
We review here {it Maximum Caliber} (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of {it Maximum Entropy} (Max Ent) is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of Non-Equilibrium Statistical Physics -- such as the Green-Kubo fluctuation-dissipation relations, Onsagers reciprocal relations, and Prigogines Minimum Entropy Production -- are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give recent examples of MaxCal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle, and some limitations.
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