Stochastic Thermodynamics


CALL: 2013

DOMAIN: MS - Materials, Physics and Engineering

FIRST NAME: Massimiliano

LAST NAME: Esposito



HOST INSTITUTION: University of Luxembourg


START: 2014-01-01

END: 2017-12-31


Submitted Abstract

It is seldom that a basic law of physics is put into a totally new perspective. This has happened with the second law of thermodynamics over the past decade. In the standard formulation, the total entropy change S has to be non-negative. For small systems, one can define a stochastic entropy s, which coincides with the usual entropy on average, < s >= S. While the change of this quantity s can be negative, the second law is replaced by a more profound statement, namely that the probability to observe an increase s > 0 is exponentially larger than the probability to observe a corresponding decrease -s, explicitly: P(s) = exp(s)P(-s). This equality, the so-called detailed fluctuation theorem, implies another equality, the so-called integral fluctuation theorem, < exp(-s) >= 1, which in turn implies the inequality < s > 0, corresponding to the usual second law of thermodynamics. Depending on the specific context of the problem, the detailed and integral fluctuation theorem can be rewritten under various forms, the best known being the Crook’s relation and the Jarzynski equality for a system in contact with a single heat bath. Here the total entropy change is s = (w – F)/T with w the work needed to move the system between two different equilibrium states with free energy difference F.In view of the momentous implications of the second law, we can expect that this new formulation will have important consequences, especially in the context of small systems where fluctuations cannot be ignored. Our main scientific purpose is to illustrate further the wide applicability of the new approach by developing new technical and conceptual tools, which extend the existing ones from standard thermodynamics, but also include novel insights specific for the new formalism. On the technical side, we mention the development of a perturbation expansion around equilibrium (the so-called low dissipation limit), the formulation of other stochastic thermodynamic potentials (for example the stochastic analogues of the standard thermodynamic potentials) and the discussion of exactly solvable cases. As an example of a novel application, we cite the theory of logic computation. It is in principle possible to perform logic operations reversibly, and this issue has – to some extent – been investigated using traditional thermodynamics. But it will be even more valuable to investigate the trade-off between speed, accuracy and dissipation away from the reversible regime, something which can be done explicitly in stochastic thermodynamics. Similarly, reversible ratchets are able to transport particles without dissipation, albeit infinitely slowly. On the more practical side, we can evaluate and optimize the cost of stochastic transport. As a side-issue we mention that reversible ratchets are characterized by a geometric phase, analogous to the famous Berry phase from quantum mechanics. We will use stochastic thermodynamics to find an interpretation of this phase for reversible ratchets. Finally we will explore the macroscopic limit of stochastic thermodynamics, which will clarify further the connection with traditional thermodynamics. This analysis will be especially interesting in models displaying phase transitions. Stochastic thermodynamics should reveal in particular the specificity of nonequilibrium transitions and the role of fluctuations in finite size systems. This work will be performed in collaboration with Dr. M. Esposito at the University of Luxembourg where he received a prestigious ATTRACT fellowship a year ago and has built a new research group focusing on topics closely related to the present proposal. Hence, the main purpose of this research project is to pursue the intense and very pro-ductive scientific collaboration that has taken place over the last four years between M. Esposito and myself in the context of a research project sponso

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