Special CPM Seminar

Entropy production and fluctuation relations in thermodynamics of small non-Markovian systems

Tapio Ala-Nissila

Aalto University School of Science

Fluctuation relations provide a powerful formalism to study the stochastic nature of fluctuating thermodynamic variables, such as (free) energy, entropy, heat and work in small systems driven beyond the linear response regime. Most of work done to date in this field has been done within the context of the Markovian approximation, where the system has no memory of its previous states. However, it is easy to argue that in reality many interacting systems become non-Markovian when driven out of equilibrium. I will present some new results for the fluctuation relations, and entropy, heat and work production in a system of driven single-electron transitions (the “single-electron box”), which becomes non-Markovian due to excess heat dissipation [1], or which can be driven to a steady-state non-equilibrium state [2]. I will also discuss the relationship between different sources of entropy generation in non-Markovian systems using the driven SEB as a benchmark [3].

[1] J.P. Pekola, A. Kutvonen, and T. A-N., JSTAT P02033 (2013).
[2] J.V. Koski, T. Sagawa, O-P. Saira, Y. Yoon, A. Kutvonen, P. Solinas, M. Möttönen, T.A-N., and J.P. Pekola, Nat. Phys. 9, 644 (2013).
[3] A. Kutvonen, J.P. Pekola, and T. A-N., Entropy production in a non-Markovin environment, arXiv:1408.3020i (2014).