Language-Based Information Erasure

Making use of the equivalence between information and entropy, we have shown in a recent paper that particles moving with a kinetic energy ε carry potential information i p o t ( ε , T ) = 1 ln ( 2 ) ε k B T relative to a heat reservoir of temperature T . In this paper we build on this result and consider in more detail the process of information gain in photon detection. Considering photons of energy E p h and a photo-ionization detector operated at a temperature T D , we evaluate the signal-to-noise ratio S N ( E p h , T D ) for different detector designs and detector operation conditions and show that the information gain realized upon detection, i r e a l ( E p h , T D ) , always remains smaller than the potential information i p o t ( E p h , T D ) carried with the photons themselves, i.e.,: i r e a l ( E p h , T D ) = 1 ln ( 2 ) ln ( S N ( E p h , T D ) ) ≤ i p o t ( E p h , T D ) = 1 ln ( 2 ) E p h k B T D . This result is shown to be generally valid for all kinds of technical photon detectors, which shows that i p o t ( E p h , T D ) can indeed be regarded as an intrinsic information content that is carried with the photons themselves. Overall, our results suggest that photon detectors perform as thermodynamic engines that incompletely convert potential information into realized information with an efficiency that is limited by the second law of thermodynamics and the Landauer energy bounds on information gain and information erasure.

Download Full-text

Feedback traps for virtual potentials

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2016.0217 ◽

2017 ◽

Vol 375 (2088) ◽

pp. 20160217 ◽

Cited By ~ 5

Author(s):

Momčilo Gavrilov ◽

John Bechhoefer

Keyword(s):

Optical Tweezers ◽

Single Molecule ◽

Feedback Loop ◽

Target Object ◽

Optical Forces ◽

First Law Of Thermodynamics ◽

Average Work ◽

Arbitrary Potential ◽

Information Erasure ◽

Long Protocol

Feedback traps are tools for trapping and manipulating single charged objects, such as molecules in solution. An alternative to optical tweezers and other single-molecule techniques, they use feedback to counteract the Brownian motion of a molecule of interest. The trap first acquires information about a molecule's position and then applies an electric feedback force to move the molecule. Since electric forces are stronger than optical forces at small scales, feedback traps are the best way to trap single molecules without ‘touching’ them (e.g. by putting them in a small box or attaching them to a tether). Feedback traps can do more than trap molecules: they can also subject a target object to forces that are calculated to be the gradient of a desired potential functionU(x). If the feedback loop is fast enough, it creates avirtual potentialwhose dynamics will be very close to those of a particle in an actual potentialU(x). But because the dynamics are entirely a result of the feedback loop—absent the feedback, there is only an object diffusing in a fluid—we are free to specify and then manipulate in time an arbitrary potentialU(x,t). Here, we review recent applications of feedback traps to studies on the fundamental connections between information and thermodynamics, a topic where feedback plays an even more fundamental role. We discuss how recursive maximum-likelihood techniques allow continuous calibration, to compensate for drifts in experiments that last for days. We consider ways to estimate work and heat, using them to measure fluctuating energies to a precision of ±0.03kTover these long experiments. Finally, we compare work and heat measurements of the costs of information erasure, theLandauer limitofkTln 2 per bit of information erased. We argue that, when you want to know the average heat transferred to a bath in a long protocol, you should measure instead the average work and then infer the heat using the first law of thermodynamics.This article is part of the themed issue ‘Horizons of cybernetical physics’.

Download Full-text