A Cost/Speed/Reliability Tradeoff to Erasing

We present a Kullback–Leibler (KL) control treatment of the fundamental problem of erasing a bit. We introduce notions of reliability of information storage via a reliability timescale τ r , and speed of erasing via an erasing timescale τ e . Our problem formulation captures the tradeoff between speed, reliability, and the KL cost required to erase a bit. We show that rapid erasing of a reliable bit costs at least log 2 - log 1 - e - τ e τ r > log 2 , which goes to 1 2 log 2 τ r τ e when τ r > > τ e .

[1]  Michael Benjamin Propp,et al.  The thermodynamic properties of Markov processes , 1985 .

[2]  H. Kappen.  Linear theory for control of nonlinear stochastic systems. , 2004, Physical review letters.

[3]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[4]  Stefan Schaal,et al.  Reinforcement Learning With Sequences of Motion Primitives for Robust Manipulation , 2012, IEEE Transactions on Robotics.

[5]  Hilbert J. Kappen,et al.  Graphical Model Inference in Optimal Control of Stochastic Multi-Agent Systems , 2008, J. Artif. Intell. Res..

[6]  Vicenç Gómez,et al.  Optimal control as a graphical model inference problem , 2009, Machine Learning.

[7]  Rob R. de Ruyter van Steveninck,et al.  The metabolic cost of neural information , 1998, Nature Neuroscience.

[8]  John A. Swanson,et al.  Physical versus Logical Coupling in Memory Systems , 1960, IBM J. Res. Dev..

[9]  Massimiliano Esposito,et al.  Second law and Landauer principle far from equilibrium , 2011, 1104.5165.

[10]  Peter Salamon,et al.  Finite time optimizations of a Newton’s law Carnot cycle , 1981 .

[11]  K. Sekimoto.  Kinetic Characterization of Heat Bath and the Energetics of Thermal Ratchet Models , 1997 .

[12]  M. Esposito,et al.  Finite-time erasing of information stored in fermionic bits. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S. Mitter,et al.  Optimal control and nonlinear filtering for nondegenerate diffusion processes , 1982 .

[14]  H. Kappen.  Path integrals and symmetry breaking for optimal control theory , 2005, physics/0505066.

[15]  Robert Alicki.  Information is not physical , 2014 .

[16]  Robert Aebi.  Schrödinger Diffusion Processes , 1996 .

[17]  A. Beurling,et al.  An Automorphism of Product Measures , 1960 .

[18]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[19]  A D Wissner-Gross,et al.  Causal entropic forces. , 2013, Physical review letters.

[20]  R. Zwanzig.  Nonequilibrium statistical mechanics , 2001, Physics Subject Headings (PhySH).

[21]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[22]  Manoj Gopalkrishnan.  The Hot Bit I: The Szilard-Landauer Correspondence , 2013, ArXiv.

[23]  Hilbert J. Kappen,et al.  Stochastic Optimal Control in Continuous Space-Time Multi-Agent Systems , 2006, UAI.