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Extracting work from a single heat bath - A case study on Brownian particle under external magnetic field in presence of information

Work can be extracted from a single bath beyond the limit set by the second law by performing measurement on the system and utilising the acquired information. As an example we studied a Brownian particle confined in a two dimensional harmonic trap in presence of magnetic field, whose position co-ordinates are measured with finite precision. Two separate cases are investigated in this study - (A) moving the center of the potential and (B) varying the stiffness of the potential. Optimal protocols which extremise the work in a finite time process are explicitly calculated for these two cases. For Case-A, we show that even though the optimal protocols depend on magnetic field, surprisingly, extracted work is independent of the field. For Case-B, both the optimal protocol and the extracted work depend on the magnetic field. However, the presence of magnetic field always reduces the extraction of work.