Thermodynamics of micro and nano-scale systems exhibits distinctly different features from that of large systems due to influence of large thermal fluctuations . Typical energy changes of these systems are of the order of thermal energy per degree of freedom. Consequently a new thermodynamics named stochastic energetics has been developed recently to analyze these system theoretically. We have performed an extensive analysis of a single-particle stochastic heat engine constructed by manipulating Brownian particle in a time-dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values even in the quasistatic regime. Their distributions show power law tails, however the exponents are not universal. We have also verified fluctuation relations for heat engines in time periodic steady state. Work can be extracted from a single bath beyond the limit set by the second law of thermodynamics by performing measurement on the system and utilizing the acquired information. This imposes an upper bound on extracted work and maintains a generalized (i.e., with information) second law. As an example, we studied a Brownian particle confined in a two-dimensional harmonic trap in the presence of a magnetic field, whose position coordinates 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 that extremize the work in a finite-time process are explicitly calculated for both these cases. The second law can be apparently violated again when an information reservoir is used to modify the performance of an machine. We have developed an autonomous Maxwell demon information machine where the system (demon) is coupled to a memory register (tape), a work source and two heat baths. The performance of the system depends on the interplay between the two sources along with the heat baths. We have found that the system can act as an engine, refrigerator or an eraser. Even the combination of any two is possible in some parameter space. We have achieved an efficiency of the engine greater than the Carnot limit on average. The coefficient of performance of the refrigerator is also larger than the Carnot limit.
Photon Bose-Einstein condensates are an interesting platform from which to study near-thermal equilibrium. They offer many advantages over atomic and solid state systems due to the easy preparation and measurement of photons. I will present a non-equilibrium model, derived from a Hamiltonian, capable of predicting the photon populations within a factor of two. This model makes the counter intuitive prediction that the photonic modes may loose condensation as the pump power is increased. The complex interaction between modes produces a rich phase diagram, which I have fit analytic results to.
Bose-Einstein condensation has been observed with cold atomic gases, exciton-polaritons, and more recently with photons in a dye-solution filled optical microcavity. I will here describe measurements of my Bonn group observing the transition between usual lasing dynamics and photon Bose-Einstein condensation. The photon Bose-Einstein condensate is generated in a wavelength-sized optical cavity, where the small mirror spacing imprints a low-frequency cutoff and photons confined in the resonator thermalize to room temperature by absorption re-emission processes on the dye molecules. This allows for a particle-number conserving thermalization, with photons showing a thermodynamic phase transition to a macroscopically occupied ground state, the Bose-Einstein condensate. When the thermalization by absorption and re-emission is faster than the photon loss rate in the cavity, the photons accumulate at lower energy states above the cavity cutoff, and the system finally thermalizes to a Bose-Einstein condensate of photons. On the other hand, for a small reabsorption with respect to the photon loss, the state remains laser-like. I will also report recent measurements of the heat capacity of the photon gas, which were performed under the conditions of the thermalization being much faster than both photon loss and pumping. At the Bose-Einstein phase transition, the observed specific heat shows a cusp-like singularity, as in the $\lambda$-transition of liquid helium, illustrating critical behavior of the photon gas. In my talk, I will begin with a general introduction and give an account of current work and future plans of the Bonn photon gas experiment.