Ritam Basu supervised by Dr. Samyadeb Bhattacharya  received his Master of Science  in Computer Science and Engineering (CSE). Here’s a summary of his research work on Dynamical Aspects of Ergodic Quantum Channels:

 In this work, we introduce and rigorously characterize a broad class of quantum operations termed quantum ergodic channels. These are completely positive, and trace-preserving (CPTP) maps that possess a unique fixed point toward which any initial quantum state asymptotically evolves. The existence of such a fixed point enables a systematic exploration of ergodicity in quantum dynamics, extending classical notions into the quantum regime.

 We construct and analyze Lindblad-type master equations governing the evolution under these ergodic channels in arbitrary finite-dimensional Hilbert spaces. These equations describe both Markovian and non-Markovian dynamics, depending on the time dependence and structure of the generator. In particular, the class of ergodic channels considered here encompasses both memoryless and memory-affected evolution, allowing us to explore their differences through established quantitative measures of non-Markovianity.

 A special focus is placed on the case where the fixed point of the channel is a passive state, i.e., a state from which no work can be extracted via unitary operations. In such settings, evolution under ergodic channels gives rise to non-trivial ergotropy dynamics. Ergotropy is a fundamental thermodynamic quantity that quantifies the maximum extractable work from a quantum state via unitary transformations, assuming no access to additional resources. We show that in the Markovian regime, where the dynamics lack memory, the ergotropy of the system decreases monotonically over time, consistent with the second law of thermodynamics in open systems.

However, under non-Markovian dynamics, the situation changes significantly. We demonstrate that ergotropy can temporarily increase during evolution, indicating a backflow of useful energy from the environment into the system. This phenomenon—referred to as ergotropy backflow—is a direct manifestation of memory effects and points to the possibility of temporary reversals in the degradation of thermodynamic resources. Our analysis shows that this backflow is not only physically meaningful but also operationally relevant: it can serve as a dynamical witness or indicator of non-Markovianity.

These findings offer a novel perspective on the interplay between non-Markovianity and thermodynamic behavior in open quantum systems. By grounding the discussion in well defined resource-theoretic and thermodynamic terms, this study deepens our understanding of how memory effects influence the evolution of quantum resources such as ergotropy. In particular, it highlights the role of ergodic channels as a versatile theoretical framework for studying energy dynamics, dissipation, and resource recovery in realistic quantum settings—including potential applications in the design and analysis of quantum batteries.

 Overall, the results presented here enrich the theoretical framework of open quantum systems and pave the way for future investigations into the thermodynamic implications of quantum memory effects. They suggest practical strategies for identifying, characterizing, and potentially exploiting non-Markovian dynamics to enhance the performance of emerging quantum technologies. 

July 2025