Cyclic Heat Engines in Stochastic Thermodynamics

Study of macroscopic cyclic heat engines and refrigerators have been a major motivation for the emergence of thermodynamics. In the last decade, cyclic heat engines that have large fluctuations and operate at finite time were studied within the more modern framework of stochastic thermodynamics. This thesis is concerned with such cyclic heat engines. We have obtained original results in three different aspects of this topic.

First, the concept of cyclic active heat engines for a system in the presence of hidden dissipative degrees of freedom, also known as a non-equilibrium or active reservoir, has also been studied in theory and experiment. Such active heat engines have shown efficiencies that have apparently surpassed the Carnot limit, and hence “violated” the universal second law of thermodynamics. In this thesis, we have derived a new second law that does not depend on the heat dissipation of an active engine and can be calculated from experimentally observable degrees of freedom. The new second law has an information theoretic term that helps us to explain how the Carnot limit has not been violated in active engines. To obtain a second law expressed in terms of observable variables in the presence of hidden degrees of freedom we introduce a coarse-grained excess entropy and prove a fluctuation theorem for this quantity.

Second, building up on the second law we derived for active heat engines, we propose the concept of an active refrigerator.
We show that active refrigerators can perform tasks beyond its traditional limits for refrigerator. For instance, using a simple model system, we obtain analytical results that demonstrate active refrigerators can surpass the performance of standard passive refrigerators. In particular, active refrigerators can function without any work input, and even they can simultaneously extract heat like a refrigerator and extract work like an engine.

In this thesis, the role of interactions on cyclic stochastic engines has also been explored via an Ising model heat engine. We have used one-dimensional and mean field Ising models to demonstrate how interactions help a heat engine to perform better. We also find that due to phase transition phenomena, the engine exhibits a novel behaviour where it can operate without the magnetic field in a part of the protocol.