Fluctuation Relations and the Foundations of Statistical Thermodynamics: A Deterministic Approach and Numerical Demonstration

The fluctuation theorem and the work relation are exact nonequilibrium thermodynamic relations developed almost two decades ago. In the intervening time, these relations have been applied to prove a number of new theorems, including the dissipation theorem, the relaxation theorem, the maximum likelihood estimator, and various phase function representations. They can also be applied to provide a proof of Boltzmann's postulate of equal a priori probability and a proof of the relationship between the phase space volume, the physical volume, the energy, and the thermodynamic entropy and temperature for the equilibrium microcanonical ensemble. Here, we take one of the systems used to study these relations, the optical trapping system, and demonstrate the various results for one conceptually simple system.