1. Thermodynamics and Information Alex Thompson Phys 495, UW, Autumn 2015

2. Overview -History (Maxwell, Szilard, Shannon, Landauer) -Theory ( built into the above ) Experimental tests – Information ratchets – Landauer’s principle Key sources: – Toyabe, et. al (2010) – Berut, et al. (2012)

3. Maxwell’s Demon Gedanken experiment: – Trapdoor between two sides of a partitioned box filled with a gas – Perfect knowledge of kinematics allows separation of fast from slow particles – Information drives system out of equilibrium – Temperature difference can drive a heat engine. Image: http://cdn.phys.org/newman/gfx/news/hires/2009/maxwellsdemon.jpg

4. Shannon Entropy Shannon’s information-theoretic entropy (1948): From thermodynamics (Gibbs Entropy): Thermodynamic and informational entropy…same form!

5. Szilard Engine 1929: – 1. Divide box’s volume – 2. Measure location of particle; hook up cable to particle’s side – 3. Allow isothermal expansion of single-particle gas – 4. W = kT ln(2) extracted from a single temperature reservoir! Is the second law broken??? Image: http://www.theo2.physik.uni-stuttgart.de/forschung/stochasticthermodynamics/

6. Landauer’s Principle & Erasure 1961: Rolf Landauer: Information states map to physical states. Erasing a group of bits reduces number of logical, thus physical states. Decrease in memory microstates  entropy of memory decreases… Entropy of universe increases… heat must be generated! Minimum heat produced by erasing one bit of classical information: Image: http://www.nature.com.offcampus.lib.washington.edu/nature/journal/v483/n7388/fig_tab/nature10872_F1.html

7. Landauer’s Principle & Erasure 1982, Charles Bennett: Full cycle of Szilard’s engine requires erasure. Erasure releases Q = kT ln(2), offsets info storage’s reduction in entropy Note: measurement is logically and thermodynamically reversible

8. Reformulation of the second law Sagawa and Ueda, 2008: Where I is the mutual information, between measured system feedback controller.

9. Information Engine Experiment of Toyabe,et al. 2010 – Colloidal particle in an optical trap – With CCD camera, observe fluctuations – When particle’s potential increases, change phase of E field = insert optical barrier – “Information Ratchet” – Derive useful work from feedback on constant temperature system! Image: http://www.nature.com.offcampus.lib.washington.edu/nphys/journal/v6/n12/fig_tab/nphys1821_F1.html

10. Information Engine a) Experimental setup b) trapping potential(s) c) feedback control Feedback: 1. Measure particle. 2. If near a peak in current potential, wait for seconds. 3. Rotate potential 180 degrees. If is short, particle’s potential increases

11. Testing Landauer’s Principle Bérut, et al. 2012: – Particle trapped in double well – Reduce potential barrier, raise same side each time – Deform potential back to original shape Particle ends in same well with probability near 1 In the limit of long erasure time, results converge toward, but do not drop below Landauer’s limit!

12. Extensions Landauer’s principle applies to any logically irreversible process – (Mapping multiple input states to a single output) – AND, OR, NAND, XOR, etc. – All of these processes are also thermodynamically irreversible! ?

13. Applications Many in biology/biophysics: – Computation of energy costs of computing intercellular chemical concentrations limited by energy consumption of cells – Cellular motors switch directions based on protein concentrations; switching statistics emerge from modeling informational-energetic cost of sensing and switching.

14. Additional Sources to explore: ** Physics Today “Information: From Maxwell’s demon to Landauer’s eraser ”, Sept. 2015 http://www.nature.com/nphys/journal/v11/n2/full/nphys3230.html#information-and-the-second-law http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.113.030601 The Physics of Forgetting (2001 Contemporary Physics) http://www3.imperial.ac.uk/pls/portallive/docs/1/55905.PDF http://www3.imperial.ac.uk/pls/portallive/docs/1/55905.PDF Principle of Maximum Fischer Information from Hardy’s Axioms applied to statistical systems http://journals.aps.org/pre/pdf/10.1103/PhysRevE.88.042144 http://journals.aps.org/pre/pdf/10.1103/PhysRevE.88.042144 M. G. Raizen, Science 324, 1403 (2009) ** Toyabe, et. al (2010): http://www.nature.com/nphys/journal/v6/n12/abs/nphys1821.htmlhttp://www.nature.com/nphys/journal/v6/n12/abs/nphys1821.html ** Berut, et al. (2012): http://www.nature.com/nature/journal/v483/n7388/full/nature10872.htmlhttp://www.nature.com/nature/journal/v483/n7388/full/nature10872.html ** Sagawa and Ueda: Phys. Rev. Let. 104 090602 (2010): http://arxiv.org/pdf/0907.4914v3.pdfhttp://arxiv.org/pdf/0907.4914v3.pdf Jarzynski 2014 phys. Today article on Maxwell’s demon experiments http://www.chem.umd.edu/wp- content/uploads/2012/12/Lu_Mandal_Jarzynski_PhysToday_67_August_p60_2014.pdfhttp://www.chem.umd.edu/wp- content/uploads/2012/12/Lu_Mandal_Jarzynski_PhysToday_67_August_p60_2014.pdf Jarzynski (contains explanation of his work and other noneq. Dynamics http://www.chem.umd.edu/wp- content/uploads/2012/12/Jarzynski_AnnuRevCondMattPhys_2_329_20111.pdfhttp://www.chem.umd.edu/wp- content/uploads/2012/12/Jarzynski_AnnuRevCondMattPhys_2_329_20111.pdf Seifert 2014 Stochastic Thermodynamics, fluctuation theorems, and molecular machines http://arxiv.org/abs/1205.4176 …. https://www.youtube.com/watch?v=YKnP0SJTZfU&ab_channel=InternationalCentreforTheoreticalScience s http://arxiv.org/abs/1205.4176 https://www.youtube.com/watch?v=YKnP0SJTZfU&ab_channel=InternationalCentreforTheoreticalScience s ** Denotes source mentioned in talk