Non-Markovian environments and information exchange in stochastic thermodynamics

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Aki Kutvonen Name of the doctoral dissertation Non-Markovian environments and information exchange in stochastic thermodynamics Publisher School of Science Unit Department of Applied Physics Series Aalto University publication series DOCTORAL DISSERTATIONS 15/2016 Field of research Theoretical and Computational Physics Manuscript submitted 17 November 2015 Date of the defence 5 February 2016 Permission to publish granted (date) 22 December 2015 Language English Monograph Article dissertation (summary + original articles) Abstract The current challenge in the field of thermodynamics is to extend the fundamental laws of thermodynamics to small non-equilibrium systems. The framework of stochastic thermodynamics has proven useful in studying small systems, which often are fluctuating and easily driven out of equilibrium. In stochastic thermodynamics the fundamental laws are formulated using fluctuating and trajectory dependent variables such as entropy, heat and work evolving under stochastic equations of motion. More recently, the possibility to manipulate small systems by performing measurements and feedbacks has also been included in the thermodynamic framework. In this thesis, stochastic thermodynamics and thermodynamics of information are studied using physically feasible model systems based on single electron tunneling at low temperatures. We study dissipation, entropy production, and thermodynamics of information in these setups analytically and by using Monte Carlo simulations and numerically solving master equations. We develop a model of non-Markovian dynamics, in which the system and the environmental degrees of freedom are correlated during the process. This model explains the sources of additional entropy production, not included in the standard stochastic thermodynamics description, and it can be realized in the operation of a voltage driven single electron box. Furthermore, we introduce two different model setups, where dissipation can be made negative, and thus the setups operate as Maxwell's demons. In both setups, the role of information is quantitatively characterized. The research presented in the thesis develops the field of thermodynamics at small scales into a more quantitative and accurate direction, where interaction energies and non-equilibrium excitations in the environment are taken into account. Furthermore, the results provide a step towards more precise modeling, understanding, and design of small scale devices, where dissipation and fluctuations play a major role.The current challenge in the field of thermodynamics is to extend the fundamental laws of thermodynamics to small non-equilibrium systems. The framework of stochastic thermodynamics has proven useful in studying small systems, which often are fluctuating and easily driven out of equilibrium. In stochastic thermodynamics the fundamental laws are formulated using fluctuating and trajectory dependent variables such as entropy, heat and work evolving under stochastic equations of motion. More recently, the possibility to manipulate small systems by performing measurements and feedbacks has also been included in the thermodynamic framework. In this thesis, stochastic thermodynamics and thermodynamics of information are studied using physically feasible model systems based on single electron tunneling at low temperatures. We study dissipation, entropy production, and thermodynamics of information in these setups analytically and by using Monte Carlo simulations and numerically solving master equations. We develop a model of non-Markovian dynamics, in which the system and the environmental degrees of freedom are correlated during the process. This model explains the sources of additional entropy production, not included in the standard stochastic thermodynamics description, and it can be realized in the operation of a voltage driven single electron box. Furthermore, we introduce two different model setups, where dissipation can be made negative, and thus the setups operate as Maxwell's demons. In both setups, the role of information is quantitatively characterized. The research presented in the thesis develops the field of thermodynamics at small scales into a more quantitative and accurate direction, where interaction energies and non-equilibrium excitations in the environment are taken into account. Furthermore, the results provide a step towards more precise modeling, understanding, and design of small scale devices, where dissipation and fluctuations play a major role.