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Introduction to Statistical Thermodynamics of Soft and Biological Matter

Introduction to Statistical Thermodynamics of Soft and Biological Matter. Dima Lukatsky FOM Institute for Atomic and Molecular Physics [AMOLF], Amsterdam Email: Lukatsky@amolf.nl. Acknowledgements: Samuel Safran, Weizmann Institute of Science

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Introduction to Statistical Thermodynamics of Soft and Biological Matter

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  1. Introduction to Statistical Thermodynamics of Soft and Biological Matter Dima Lukatsky FOM Institute for Atomic and Molecular Physics [AMOLF], Amsterdam Email: Lukatsky@amolf.nl Acknowledgements: Samuel Safran, Weizmann Institute of Science Daan Frenkel, FOM-AMOLF

  2. References • Statistical Thermodynamics of Surfaces, • Interfaces and Membranes • S. A. Safran, (Addison Wesley, 1994). • Biological Physics. Energy, Information, Life • Philip Nelson, (Freeman and Company, New York, 2004). • Understanding Molecular Simulations • D. Frenkel and B. Smit (Academic, 2002). • Intermolecular and Surface Forces • J. Israelachvili, (Academic, 1992). • The Colloidal Domain: Where Physics, • Chemistry, Biology and TechnologyMeet • F. Evans and H. Wennerstrom, (Wiley, 1994).

  3. Main Questions and Ideas • How can living organisms be so highly ordered ? • Equilibrium versus non-equilibrium systems. Living systems • are not at equilibrium, and they are open. Quasi equilibrium. • Interactions can lead to a spontaneous ordering even • at equilibrium. • Entropy can lead to a spontaneous ordering at equilibrium ! • Flow of information characterizes living organisms. • Evolution is the biological “pressure”. • Living organisms are robust.

  4. Self-assembly High specificity Multi-component Information Biology is living soft matter

  5. - characteristic energy scale 100 nm 1 mm = 1000 nm 2 nm E. coli Bacteriophage virus 170.000 bp DNA 25 nm DNA microtubule Thermal energy and molecular length-scale - Boltzmann constant

  6. If everything is so random in the nano-world of cells, how can we say anything predictive about what’s going there ? M.W. Davidson, FSU Statistical description of random World The collective activity of many randomly moving objects can be effectively predictable, even if the individual motions are not.

  7. Entropy. The 2nd law of thermodynamics Isolatedsystem always evolve to thermodynamic equilibrium. In equilibrium isolated system has the greatest possible ENTROPY (disorder*) allowed by the physical constraints on the system. * Sometimes, high entropy means more order!

  8. Number of allowed states in B: Number of allowed states in A: Number of allowed states in joint systemA+B: Entropy: Entropy is additive: Entropy as measure of disorder

  9. Molecules A Molecules B Entropy of system: Using Stirling formula: Probability of each state: How to count states Total number of states:

  10. Probability of each state: Entropy… Molecules A Molecules B

  11. Sequence Analysis Course… Lecture 9 Shannon definition INFORMATION ENTROPY

  12. For one molecule: V – total volume - “cell” volume (quantum uncertainty ) For N molecules: Indistinguishablility Free energy of ideal gas: density: Entropy of ideal gas

  13. So what IS entropy? So what IS entropy?

  14. The Entropy is equal to …. Ludwig Boltzmann

  15. The logarithm of the number of states … Ludwig Boltzmann

  16. Times My constant! Ludwig Boltzmann

  17. During a spontaneous change in a closed system, the DISORDER increases …. WATCH OUT! FAKE Second Law

  18. Disordered Liquid Ordered Solid

  19. Lower Entropy… Higher Entropy… Hard-sphere liquid Hard-sphere freezing is driven by entropy ! Hard-sphere crystal

  20. OPAL Colloidal “Entropic” crystal

  21. Total energy: Number of allowed states in A Total number of allowed states System B System A Total entropy Entropy and Temperature Isolated (closed) system:

  22. Total energy: Define Temperature: Entropy Maximization A and B in thermal contact. Total system A+B is isolated. System B System A Total entropy:

  23. Equilibration Ordering and 2nd law of thermodynamics System in thermal contact with environment Cools to room Initially high • Condensation into liquid (more ordered). • Entropy of subsystem decreased… • Total entropy increased! Gives off heat to room.

  24. For closed system: For open (small) system Free energy is minimized: - Helmholtz free energy - Gibbs free energy Free energy Small system a Reservoir, T

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