In this thesis we have thermodynamically characterized finite time processes performed on a colloidal particle, kept in contact with thermal reservoir(s). Thermodynamic processes are implemented on the colloidal particle by systematically changing the confining potential in a time dependent way, according to an external driving protocol or by controlling the environmental conditions over a finite duration. First, we study two externally driven systems: one in which the driving is deterministic, and another where the driving is stochastic. These models have appeared in the literature as the building blocks of microscopic machines such as Brownian heat engines and are hence of interest to analyze. In particular, it is of interest to understand the distribution of work done by the colloidal particle as well as the distribution of heat dissipated. These distributions are known in all generality only in a very few cases. In the work we present here, we determine exactly the asymptotic forms of the work distributions (for a finite time duration of the process), which is shown to have non-Gaussian fluctuations. We also find a method to obtain the exact moment generating function of the work distribution, using which we can explicitly calculate aspects of a recently discovered relation for non-equilibrium systems, namely the thermodynamic uncertainty relation. To our knowledge, our model provides the only non-trivial example of a system where the uncertainty relation can be investigated exactly for all times. We have studied the system in various temporal regimes, and have found interesting features such as a time of minimum uncertainty, which may be relevant for the functioning of microscopic machines. Finally, we discuss, an experimentally realized colloidal heat engine model which consists of a single colloidal particle as the working substance. Exact finite time statistics can be obtained for this model using the methods we discuss in the thesis. We present our preliminary results illustrating this.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:su-155316 |
| Date | January 2018 |
| Creators | K. Manikandan, Sreekanth |
| Publisher | Stockholms universitet, Fysikum |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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