In contrast to their macroscopic counter parts (such as car engines or refrigerators), these small scale machines are prone to thermal fluctuations. As a consequence, the functioning of these machines is no longer deterministic but rather stochastic, with the performance varying from realization to realization. Results of a recent study by physicists from Stockholm University in collaboration with researchers at Nordita and the University of Bielefeld, provide a general understanding of the efficiency fluctuations in microscopic machines and have now appeared in Physical Review Letters (Phys. Rev. Lett. 122, 140601). The authors have identified typical long-time features of the fluctuating efficiency in thermal environments, that are independent of system specific details.

Classical thermodynamics originated from an attempt to understand and build optimally performing engines. For macroscopic heat engines working in contact with a hot (Th) and a cold (Tc) reservoir, it is known that the maximum efficiency attainable is the Carnot efficiency ( η C = 1 - Tc/Th). It is then natural to ask what happens to such limitations at small scales. A break through advancement came following the discovery of non equilibrium fluctuation relations that generalized the macroscopic second law, and thereby concepts from classical equilibrium thermodynamics, to small, far from equilibrium systems. Now we understand that quantities, such heat absorbed, work done and hence also the efficiency of a heat engine, can be defined even for non-equilibrium systems and are moreover, statistical in nature. Recent theoretical as well as experimental advancements such as micro manipulation techniques have enabled us to both build and analyze miniature versions of such engines to understand these features better. These systems have the remarkable capacity to use thermal / spatial asymmetries or other sorts of energy gradients, only relevant at small scales, to perform useful thermodynamic work.

Figure 1: A colloidal particle in an optical trap (shown as a red ball), in the presence of thermal noise, can be made to work as a microscopic machine or heat engine. Its fluctuations have some typical features, some of which are shown here. Ref: Phys. Rev. Lett. 122, 140601

A typical and well studied microscopic heat engine consists of a single colloidal particle in an aqueous solution (which acts as a thermal bath), confined using an optical trap. Such a particle can be made to do work and dissipate heat by controlling environmental conditions, the stiffness and mean position of the trap or by introducing external forces. Usually the probability distributions of the work done, heat dissipated and hence also the efficiency are hard to calculate exactly and can only be obtained within approximations. In the present work, the authors are able to exactly solve for these distributions for two non trivial setups and thereby infer some general features that an efficiency distribution should satisfy for any classical microscopic machine. An interesting new finding is that, for microscopic machines, it may be possible to reduce fluctuations and make the performance more predictable even at very large times, by fine tuning initial conditions. Since thermal fluctuations are inevitable for micro / nano scale devices, new design principles that manipulate these fluctuations to enhance the performance could be a very interesting future area of research.


Sreekanth Kizhakkumpurath Manikandan

Supriya Krishnamurthy

Efficiency Fluctuations in Microscopic Machines, Sreekanth K. Manikandan, Lennart Dabelow, Ralf Eichhorn, and Supriya Krishnamurthy., Phys. Rev. Lett. 122, 140601.