Information Thermodynamics on Feedback Process
KIAS Workshop on Quantum Information and Thermodynamics Nov, 2015, Busan Information Thermodynamics on Feedback Process Chulan Kwon Myongji University Outline Feedback process (Maxwells demon) Szilard engine Feedback by time-varying potential Cold damping Summary I. Feedback Process Inside memory device: measurement, erasure
used Bit (binary digit) Information process empty erased Hidden process erasure measurement system state measurement outcome memory state protocol, external field feedback Inside memory device: measurement, erasure At post-measurement: (Szilard) information engine Maxwells demon: violation of thermodynamic second law (1867)
Demon as a memory device: measurement-> information stored Szilard engine: tractable model (1929) Shannon entropy: Landauers principle: measurement as thermodynamic process, erasure of memory (1961) Erasure Measurement Landauers principle Bennet, others: Erasure process can resolve the paradox of demon. can be negative! Mutual information Measurement
Memory and system as a composite system (T. Sagawa and his group, since 2008) Mutual information Measurement Potential shape change depending on X will be used as a measurement error In the post-measurement process. measurement Post-measurement zero correlation zero mutual information at pre-measurement lower entropy higher mutual information at measurement higher entropy lower mutual information in post-measurement Total entropy change of the composite system and the heat bath in post-measurement Sagawa and Ueda, PRL, 2012 with the aid of fluctuation theorem Szilard engine Exorcism of demon II. Szilard Engine Revisiting: Sagawa & Ueda, PRE, 2012
Step 1: thermal equilibrium Step 2: insertion of partition and measurement Step 3: quasi-static expansion according to measurement up to volume fraction Step 4: removing partition Up to Step 3 (quasi-static)
Maximum extraction of work In sudden expansion (no work, no heat) Feedback control by time-varying potential
Revisiting: Abreu & Seifert, EPL, 2011; Sagawa & Ueda, 2012 Time-varying potential Overdamped motion Step 1: Thermal equilibrium at the beginning Step 2: Measurement Conditional probability of outcomeformeasuring Joint PDF for : PDF for Cond PDF Step 3: Switch the potential
Work done at Step 3 Step 4: protocol change in time Total work Mutual information Shannon entropy Total entropy change Quasi-static process Generalization of the optimal protocol suggested by Parrondo, Horowitz, Sagawa (Nature Phys, 2015) IV. Cold damping (with J. Um & H. Park) Kim & Qian, PRL, 2007; Jourdan et al,Nanotechnology, 2007; Ito & Sano, PRE, 2011 y E feedback v v measure Expected for other feedback processes
Repeated with time delay and interval V. Summary The thermodynamic second law should hold at any instant, not only for cycle. It was proven for a few examples via the informationthermodynamics based on the mutual information. The paradox of Maxwells demon is resolved. The feedback process for cold damping is presented.