Abstracts

1.      David Leigh (University of Edinburgh)

Exercising Demons: Synthetic Molecular Motors and Machines

 

An exciting contemporary area of chemistry is making molecules with moving parts, with the goal that they can function as nanoscopic machines capable of performing physical tasks. We will discuss some of the latest developments from our group on the introduction of ratchet principles into synthetic molecular structures, including the experimental realisation of both energy ratchets and information ratchets.

 

For some recent papers from the Leigh group see: Nature, 424, 174-179 (2003); Science, 299, 531 (2003); Science, 306, 1532-1537 (2004); Proc Natl Acad Sci USA, 102, 13378-13382 (2005); Nature Mater, 4, 704-710 (2005); Proc Natl Acad Sci USA, 103, 17650-17654 (2006); Nature, 440, 286-287 (2006); Nature, 445, 523-527 (2007). For a recent review on synthetic molecular motors and machines, see: Angew Chem Int Ed, 46, 72-191 (2007);

 

 

2. Jukka Pekola (Helsinki University of Technology)

Refrigeration, energy relaxation and thermometry in electronic mesoscopic structures

 

Metallic nanostructures at low temperatures provide a rich variety of systems where intriguing thermal and thermodynamic phenomena can be investigated [1]. Of particular interest are hybrid systems where one can combine nanoscale superconductors and usual metals, tunnel barriers and direct metallic contacts. Thermal properties of such structures are determined by the various relaxation mechanisms, for instance by electron-electron, electron-phonon, and electron-photon rates in comparison to external operation frequencies. I will discuss our earlier efforts on standard electronic refrigeration [1,2] and thermometry [1,3], and then I move to our more recent work on quantized thermal conductance [4], cyclic single-electron refrigeration [5,6] and on a Brownian refrigerator of electrons [7].

 

[1] F. Giazotto, T.T. Heikkilä, A. Luukanen, A.M. Savin, and J.P.Pekola, Rev. Mod. Phys. 78, 217 (2006).

[2] M.M. Leivo, J.P. Pekola, and D.V. Averin, Appl. Phys. Lett. 68, 1996 (1996).

[3] J.P. Pekola, K.P. Hirvi, J.P. Kauppinen, and M.A. Paalanen, Phys. Rev.

Lett. 73, 2903 (1994).

[4] Matthias Meschke, Wiebke Guichard, and Jukka P. Pekola, Nature (London) 444, 187 (2006).

[5] Jukka P. Pekola, Francesco Giazotto, and Olli-Pentti Saira, Radio-frequency single-electron refrigerator, Phys. Rev. Lett. 98, 037201 (2007).

[6] Olli-Pentti Saira, Matthias Meschke, Francesco Giazotto, Alexander M.

Savin, Mikko Möttönen, and Jukka P. Pekola, cond-mat /0702361.

[7] J.P.Pekola and F.W.J. Hekking, cond-mat/0702233.

 

 

 

3. Sandu Popescu (University of Bristol)

Entanglement and the foundations of statistical mechanics

 

Statistical mechanics is one of the most successful areas of physics. Yet, almost 150 years since its inception, its foundations and basic postulates are still the subject of debate. Here we suggest that the main postulate of statistical mechanics, the equal a priori probability postulate, should be abandoned as misleading and unnecessary. We argue that it should be replaced by a general canonical principle, whose physical content is fundamentally different from the postulate it replaces: it refers to individual states, rather than to ensemble or time averages. Furthermore, whereas the original postulate is an unprovable assumption, the principle we propose is mathematically proven. The key element in this proof is the quantum entanglement between the system and its environment. Our approach separates the issue of finding the canonical state from finding out how close a system is to it, allowing us to go even beyond the usual boltzmannian situation.

 

 

4. Stephan Grill (Max Plank Institute, Dresden)

Transcription by RNA Polymerase II

 

RNA polymerase II (RNAP II) is responsible for transcribing all mRNAs in eukaryotic cells in a highly regulated process that serves as a central control point for cellular function. We have investigated the transcription dynamics of single RNAP II molecules against force in the presence and absence of TFIIS, a transcription elongation factor that enables the enzyme to remove copy errors. Using a single- molecule dual-trap optical-tweezers assay, we found that the response of RNAP II to force is entirely determined by enzyme backtracking. We show that backtrack pause durations follow a t^−3/2 power law, implying that during backtracking RNAP II performs a random walk in discrete base-pair steps and suggesting that backtracks may account for most of RNAP II pauses. Unexpectedly, we find the polymerase to be naturally biased in the downstream direction while backtracked, possibly due to transient secondary structures that form behind the polymerase within the RNA transcript. Finally, we propose that this intrinsic force bias is a novel mechanism that is central to transcription and that acts to prevent the occurrence of fatally long pauses.

 

 

5. Udo Seifert (U. Sttutgart)

Stochastic thermodynamics: Fluctuation theorems, optimal finite-time processes and generalized Einstein relation.

 

Stochastic thermodynamics provides a conceptual framework for describing small systems embedded in a heat bath and mechanically or chemically driven to non-equilibrium. Both the first law and entropy production can be consistently defined along single trajectories. An infinity of integral fluctuation theorems hold, among which the Jarzynski relation and the one on total entropy production are prominent ones [1]. After briefly reviewing and illustrating these foundations, I will present within this scheme our recent work concerning (i) optimal finite-time processes [2] and (ii) generalized Einstein relations [3,4].

 

The optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. Explicite solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and the end of the process.

 

The Einstein relation connecting diffusion constant and mobility is violated beyond the linear response regime. We have recently derived and measured an additive correction term which involves

an integral over measurable correlation functions.

 

[1] U. Seifert, PRL 95: 040602/1-4, 2005.

[2] T. Schmiedl and U. Seifert, PRL 98: 108301/1-4, 2007.

[3] T. Speck and U. Seifert, EPL 74: 391-396, 2006.

[4] V. Blickle et al, submitted.

 

 

6. Christian Van den Broeck (U. Hasselt)

From Maxwell demon to Brownian chirality.

 

The second law of thermodynamics precludes the transformation by a single heat bath of heat into work. In the presence of two heat baths at different temperature, the rectification, even of Brownian fluctuations, becomes possible.

We present a microscopic description of such a Brownian motor. By invoking Onsager symmetry, every such motor can be transformed into a Brownian refrigerator. A rotational version of such a construction allows to define the concept of thermodynamic chirality.

 

C. Van den Broeck, R. Kawai and P. Meurs, Phys Rev Lett 93, 090601 (2004) C. Van den Broeck, P. Meurs and R. Kawai, New J Phys 7, 10 (2005) C. Van den Broeck and R. Kawai, Phys Rev Lett 96, 210601 (2006) M. Van den Broeck and C. Van den Broeck, Thermodynamic Chirality, unpublished.

 

 

7. Juan M.R. Parrondo (U. Complutense de Madrid)

Probabilistic Arrows of Time

 

Irreversibility is often thought by playing movies forward and backward in time. If one can clearly distinguish between the two, the processes in the movie are irreversible. Here we will show processes where the distinction is not so clear and can be made only in probabilistic terms. We prove that this processes are accompanied by microscopic dissipation (of order kT) and discuss their relation with the thermodynamics of computations and the Szilard engine.

 

 

8. Ryoichi Kawai (U. Alabama at Birmingham)

Dissipation Revealed in Phase Space

 

We show that an exact expression of the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states is given by <W_diss> = <W>-ΔF = kT D(ρ|ρ*) = kT <ln (ρ/ρ*)>, where ρ and ρ* are the phase space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process, respectively. D(ρ|ρ*) is the relative entropy of ρ versus ρ*. This expression is valid both in classical and quantum systems. This result also implies general inequalities, which are significantly more accurate than the second law.

 

 

9. Ken Sekimoto (U. Paris 7)

Information processing in a protein motor head

 

The goal to understand the physical process of protein motors is to relate the 3D structure of their heads with their functions. For this purpose, we propose a viewpoint of ``bidirectional control'' based on the allosteric linkages between the detection and gating within a single motor head. The application to myosin and kinesin reveals that, despite the apparent large disparity of their chemo-mechanical cycles, these motors use a very similar working principle. The finding supports further the hypothesis of the common ancesters in both structural and functional contexts.

 

 

10. Peter Reimann (U. Bielefeld)

Microcanonical typicality, the role of entanglement, and the classical limit

 

It is shown that the majority of pure states within the quantum mechanical energy shell yield expectation values for a given observable with bound spectrum which are almost indistinguishable from the microcanonical expectation value. It is argued that the basic reason behind this result is the high dimensionality of the Hilbert space describing the energy shell, while entanglement plays no significant role. In the classical limit the definition of a pure state disagrees with the one used in classical statistical mechanics, hence the above microcanonical typicality property does not apply any more classically.

 

 

11. Tehurisha Komatsu (U. Tokyo)

Nonequilibrium steady states maintained by multiple heat baths

 

We have studied a class of heat engines including Feynman's ratchet, which exhibits a directed motion of a particle in nonequilibrium steady states maintained by two heat baths. We have measured heat transfer from each heat bath separately, and found that heat transfer can be a key quantity to describe phenomena in nonequilibrium states. In this talk, we aim more general consideration about steady states of the system maintained by multiple heat baths. Starting from the frame of fluctuation theorem, we will discuss the relation between heat transfer and steady state distribution.

 

 

12. Ricardo Brito (U. Complutense de Madrid)

Heating without heat

 

Two systems at different temperatures are put in contact by means of a passive energy filter. By an appropriate choice of the filter, the two systems can heat up or cold down simultaneously wihtout any energy input.

 

 

13. Alejandro B. Kolton (U. Conplutense de Madrid)

Fluctuation theorems and disordered systems

 

We study numerically the heat fluctuations of a Brownian particle driven in a random potential, by solving simultaneously the steady-state Fokker-Planck equation and the overdamped Langevin dynamics. The total interchanged heat in a time interval, Q_tot=Q_hk+Q_ex, is analyzed in terms of the house-keeping heat Q_hk, needed to maintain detailed balance violation in a given steady state, and the excess heat Q_ex generated by arbitrarily changing some of the control parameters. In the steady-states we verify integral and detailed fluctuation theorems. By perturbing a steady state with a change of the control parameters and then by letting the system completely relax to the new (or the same) steady state, we verify the generalization of the second law - Q_ex \£ TΔS for isothermal transitions between non-equilibrium steady states. Here ΔS is the Shannon entropy difference between the final and initial steady states and the equality holds only for an adiabatic change of the control parameters. We show that disorder plays a crucial role at low temperatures in determining how slow a process must be to be considered ``adiabatic''.

 

 

14. Luis Dinis (U. Conplutense de Madrid)

Control and optimization in a collective flashing ratchet.

 

Rectification of thermal fluctuations is becoming a major topic in non equilibrium statistical mechanics, with applications in biology, condensed matter and nanotechnology. Most Brownian rectifiers work by introducing an external time-dependent perturbation, usually either a periodic or a random one, in an asymmetric equilibrium system. In this talk, I will review our results on applying external perturbations that depend on the state of the system, that is, feedback controlled perturbations, to an ensemble of Brownian particles. Two types of control protocols were studied with the aim of maximizing the flow of particles in the steady state. In the first one, the instant velocity of the center of mass is maximal at any time. This protocol is optimal for one particle but, surprisingly enough, yields worse results than a periodic or random one for large ensembles. The second protocol utilizes two control parameters and performs well for either small or large ensembles. Both protocols make use of information of the state of the system to better take advantage of fluctuations.

 

 

15. Alex Gómez-Martín (U. Barcelona)

Coarse-graining in time and space: an analytical prediction of dissipation bounds due to information loss

 

For a purely nonequilibrium mechanical system we show analytically and explicitly that the coarse-grained relative entropy provides a lower bound for the total dissipated work [1]. The expression found does not coincide with the exact calculated dissipation because only partial information about all the degrees of freedom of the system (nor the complete time history of the stochastic dynamics) is known. The sudden quench and the quasistatic limits are satisfactorily recovered by performing the nonequilibrium excursion infinitely fast and slow, respectively.

 

[1] "Dissipation: The Phase-Space Perspective", R. Kawai, J. M. R. Parrondo and C. Van den Broeck, Phys. Rev. Lett. 98, 080602 (2007).

 

 

 

16. Bart Cleuren (U. Hasselt)

Effusion of Photons and the Fluctuation Theorem

Effusion is the motion of a gas through a small opening. The discrete nature of the particles involved and their thermal motion, naturally leads to fluctuations in the outcoming flux of particles. These fluctuations, which are irrelevant in most situations, have rather intricate properties and obey the so called fluctuation theorem. We demonstrate these properties, first for an classical ideal gas, and then for a gas of photons. In the latter, the validity of the symmetry relation requires a fully quantum mechanical description of the photons which takes into account the effect of photon bunching.

 

 

17. David Andrieux (U. Libre de Bruxelles)

Irreversibility, information, and fluctuations in nonequilibrium systems

 

We investigate the time-reversal symmetry in nonequilibrium fluctuations. Their dynamical randomness can be characterized in terms of the standard and time-reversal entropies per unit time of dynamical systems theory. In particular, we present experimental results for a Brownian particle in a moving trap, showing that their difference equals the thermodynamic entropy production. Such concepts enlight the physics of information, such as Landauer's principle, with new understandings.