Studies on Space Structure, Quantum Thermodynamic Systems and Computation

Abstract

Thermodynamics is one of the core disciplines of physics, and despite its long history it happens to be a very active area of research till date. With the advent of quantum informa- tion, we have perceived that it plays a crucial role to explain the various thermodynamic phe- nomenon. The paradox of Maxwell’s demon was suitably explained with information theory. Even computation theory, whose primary motivation is to optimize the cost of computation has a direct connection with thermodynamics. The major component that a computer needs to run a process is energy, i.e., the thermodynamic cost. It got its foundation in the seminal work of Landauer, where it was commented that the computer spends kBT ln2 amount of energy to erase a bit of information (here T is the temperature of the system and kB repre- sents the Boltzmann’s constant). Thermal machines, which is one of the primary focus of thermodynamics are extensively explored for the last two centuries. It plays a major role in the development of the modern era that started with the invention of the steam engine. With the advancement in technology, we are now able to produce small devices in the nanoscale domain. We have to consider the quantum effect while analyzing the systems in this do- main. So, with the advancement of technology, the researchers got interested to analyze thermal machines in the quantum domain, giving rise to the active research area of quantum thermodynamics. In this thesis, we explore the interconnection of quantum information and thermodynamics. Here we look at what kind of thermal devices can be constructed and how quantum behavior will affect them. In this thesis, we develop the bounds on the uncertainty relation for two incompatible ob- servables for a quantum system. Having this preliminary finding, we proceed to explore the Stirling engine with the information of the uncertainty relation of the quantum system that is considered as the working medium. We are able to provide a tighter lower bound as well as propose an upper bound on the efficiency of the engine with the help of uncertainty relation without performing any measurement. We have obtained the better bounds than the previous ones by optimizing the uncertainty relation over the complete set of bases. It is explored in the non-relativistic as well as in the relativistic regime. We wanted to explore an alterna- tive approach to solve the problem as proposed: whether the change in the space structure can provide a boost to the efficiency and the coefficient of performance of thermal machines? For this purpose, we consider different quantum systems at a deformed space structure which is a generalization of the usual space structure. These quantum systems are considered as the working medium for the analysis of thermal machines like the Stirling engine and Otto engine. The prime focus has been to explore whether the change in the space structure pro- vides an advantage to the efficiency of the thermal machines over the usual space. We have done numerical analysis for deriving the solution of different equations in our work and have simulated the efficiency as well the coefficient of performance of the different thermody- namic cycles. Along with that, we have discussed a way to analyze thermodynamic cycles in a quantum computer. For the investigation of thermal machines, we need to simulate the fundamental thermodynamic process in a quantum computer. Finally, we have proposed a way to understand the black hole information paradox with the help of the pseudo density operator by simulating the system in the Rigetti quantum computer. Here in this work, we have also provided a Gedanken experiment for the exploration of gravitational waves.