1. Heat conduction induced by non-Gaussian athermal fluctuations Kiyoshi Kanazawa (YITP) Takahiro Sagawa (Tokyo Univ.) Hisao Hayakawa (YITP) 2013/07/03 Physics of Granular Flows @YITP Difference between thermal & athermal fluctuation

3. To understand small systems small systems (μm ～ nm) (Ex. Colloidal particles) → manipulation of small systems (Ex. Optical tweezers) Role of fluctuations → Feynman Ratchet (heat engine / heat conduction) Framework for small system (Theoretical limit of manipulation) Thermal noise laser

4. Analogy between Macro & Micro Macroscopic thermodynamicsMicroscopic thermodynamics macro bath & macro system Work & Heat (The 1 st law) Irreversibility (The 2 nd law) Efficiency (Carnot efficiency) macro bath & micro system (Ex) water & colloidal particle Manipulation (Optical tweezers) The 1 st & 2 nd laws? Efficiency of small systems cm order Heat Bath (Macroscopic) Macroscopic System Heat Bath (Macroscopic) Microscopic

5. Brownian particle trapped by optical tweezers (“Single particle gas”) small ⇔ compression big ⇔ expansion Colloidal particle Colloidal particle laser water

6. The 1 st law for small systems (Stochastic energetics) Environmental effect (micro degrees of freedom) K. Sekimoto, Prog. Theor. Phys. Supp. 130, 17 (1998). K. Sekimoto, Stochastic Energetics (Springer). K. Kanazawa et. al., Phys. Rev. Lett. 108, 210601 (2012).

7. The 2 nd law for small systems Average of work obeys the 2 nd law! Maximum efficiency is achieved for quasi-static processes! Colloidal particle Colloidal particle laser water

8. Heat conduction for small systems Non-equilibrium equalities Heat Average Fluctuation Fourier law Fluctuation relation

9. Brownian motor Heat Gaussian noise Detail Electrical circuits (LRC) Experimental realization (S. Ciliberto et al. (2013))

10. Summary of introduction Thermodynamics for small systems Non-equilibrium equalities

12. Thermal & athermal fluctuations Fluctuation Thermal noise (Gauss noise) Thermal fluctuation → from eq. environment Ex.)Nyquist noise Brownian noise Athermal fluctuation → from noneq. environment Ex.)Electrical shot noise Biological fluctuation Granular noise Athermal noise (Non-Gaussian)

13. Poisson noise (shot noise) E

14. Athermal env. & non-Gaussian noise Fluctuations in athermal env. ⇒ non-Gaussian noise (ii) Membrane of Red Blood Cell with ATP receptions (i) Shot & burst noise in electrical circuits Ex. ATP Athermal Env. Athermal Env. Abstraction water Non- Gaussian Thermal Env. Apply shot noise (zero-mean) Apply shot noise (zero-mean) Gaussian

15. What corrections appear in the Fourier law? Between thermal systemsBetween athermal systems Fourier law (FL) Fluctuation theorem (FT) Extension of FL & FT? Correction terms? Correction? conducting wire Athermal conducting wire

16. Non-Gaussian athermal fluctuations A conducting wire synchronizing the angles conducting wire Athermal Non-equilibrium Brownian motor Langevin Eq. Heat K. Kanazawa et. al., PRL, 108, 210601 (2012) Characterization of non-Gaussianity Non- Gaussian

17. (i) Generalized Fourier Law coupling

18. Harmonic potentialQuartic potential coupling The ordinary Fourier law Corresponding correction Correspondence

19. Numerical check of GFL (Setup) Gaussian noise (thermal) Two-sided Poisson noise (athermal) Gaussian vs. Two-sided Poisson

20. Numerical check of GFL (Results) We can change the direction of heat current by choosing an appropriate conducting wire

21. B B Ａ Ａ Ｃ Ｃ eq. (ii)Absence of the 0 th law Does the 0 th law exists? （ Equilibrium between A and B, B and C → A and C ） The direction of heat depends on the device. ← Violation of the 0 th law But, the 0 th law recovers if we fix the device. (+we can define effective temperature.) Absent for athermal systems

22. (iii) Generalized Fluctuation theorem

23. In a case of the Gaussian & two-sided Poisson noise We can further sum up the expansion! A special case of the Gaussian and two-sided Poisson noise

24. Numerical check of the linear part of the generalized fluctuation relation The Gaussian vs. two-sided Poisson case Consistent with our generalized FT not with the conventional FT Conventional Modified

25. Conclusion Generalized Fourier law Generalized fluctuation theorem Violation of the 0 st law The direction of heat depends on the contact device (If we fix the contact device, the 0 th law recovers) Non-Gaussian Brownian motor K. Kanazawa, T. Sagawa, and H. Hayakawa, Phys. Rev. E 87, 052124 (2013)