Fluctuation theorem for entropy production of a partial system in the weak coupling limit

Small systems in contact with a heat bath evolve by stochastic dynamics. Here we show that, when one such small system is weakly coupled to another one, it is possible to infer the presence of such weak coupling by observing the violation of the steady state fluctuation theorem for the partial entropy production of the observed system. We give a general mechanism due to which the violation of the fluctuation theorem can be significant, even for weak coupling. We analytically demonstrate on a realistic model system that this mechanism can be realized by applying an external random force to the system. In other words, we find a new fluctuation theorem for the entropy production of a partial system, in the limit of weak coupling.Comment: 7 pages, 3 figure

Thermodynamic uncertainty relations in a linear system

We consider a Brownian particle in harmonic confinement of stiffness $k$, in one dimension in the underdamped regime. The whole setup is immersed in a heat bath at temperature $T$. The center of harmonic trap is dragged under any arbitrary protocol. The thermodynamic uncertainty relations for both position of the particle and current at time $t$ are obtained using the second law of thermodynamics as well as the positive semi-definite property of the correlation matrix of work and degrees of freedom of the system for both underdamped and overdamped cases.Comment: Minor revision, Accepted in EPJ

Design and Analysis of a Horizontal Shaft Impact Crusher

Crusher is one of the major size reduction equipment that is used in metallurgical, mechanical, and other similar industries. They exist in various sizes and capacities which range from 0.1 ton/hr. to 50 ton/hr. They can be classified based on the degree to which they can fragment the starting material and the way they apply forces. Based on the mechanism used crushers are basically of three types namely Cone crusher, Jaw crusher and Impact crusher. Our objective is to design various components of an Impact crusher like drive mechanism, shaft, rotor, hammers, casing, and discharge mechanism which will be useful in minimizing weight, cost and maximizing the capacity and also do their analysis. Impact crushers involve the use of impact rather than pressure to crush materials. Here the material is held within a cage, with openings of the desired size at the bottom, end or at sides to allow crushed material to escape through them. This type of crusher is generally used with soft materials like coal, seeds or soft metallic ores. The mechanism applied here is of Impact loading where the time of application of force is less than the natural frequency of vibration of the body. Since the hammers/blow bars are rotating at a very high speed, the time for which the particles come in contact with the hammers is very small, hence here impact loading is applied. The shaft is considered to be subjected to torsion and bending. The grinding screen is also designed for optimal output from the crusher A performance model is also considered for the horizontal shaft impact crusher so as to find out the relation between the feed, the crusher parameters and the output parameters

Branch and Bound Technique for three stage Flow Shop Scheduling Problem Including Breakdown Interval and Transportation Time

This paper deals with minimization of the total elapsed time for nx3 flow shop scheduling problem in which the effect of breakdown interval and the transportation time are considered. A Branch and Bound technique is given to optimize the objective of minimize the total elapsed time. The algorithm is very simple and easy to understand and, also provide an important tool for decision makers to design a schedule. A numerical illustration is given to clarify the algorithm. Keywords: Flow shop scheduling, Processing time, Transportation time, Branch and Bound Technique, Optimal sequence