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In this study, we investigated the effect of long-term integrated nutrient management (INM) involving chemical fertilizers and organic amendments viz. farmyard manure (FYM), green manure (GM), and paddy straw (PS) on the availability of micronutrients in soil, their uptake by plants, and crop yield for rice-wheat system. Soil availability of micronutrients and their plant tissue concentrations was estimated in grain and straw of both the crops. Soil recovery coefficient (SRC) and transfer coefficient (TC) were calculated to find out micronutrients availability in relation to their plant uptake and transfer of micronutrients from shoot to grain, respectively. Results revealed that integration of FYM proved significantly superior to GM and PS in improving organic carbon, micronutrients availability, and shoot to grain transfer (TC) of Fe (both the crops) and Mn (wheat). Low SRC values of Zn, Cu, Fe, and Mn indicated that long-term INM can meet their plant nutritional requirement in rice-wheat system. However, higher SRC values for B (0.49) in 100% NPK treatment as well as in the integrated ones (0.22-0.27 for rice, 0.23-0.28 for wheat) suggest that quantity of this element in soil was too low to meet plants nutritional needs which was also confirmed by its very low content in the soil (below critical levels, i.e., 0.5 mg kg −1). This study concludes that long-term integration of FYM (with NPK fertilizers) has an edge over GM and PS in regulating the supply of micronutrients in soil-plant system and correcting the micronutrient deficiencies (except B) in rice-wheat cropping system.

Phosphate reactions in the soil have important implications for crop growth and its nutrition to plants. Using a 40 years old long-term fertility experiment, we studied the fate of different sources of applied P into its nutrition to wheat in calcareous soils in a pearl millet-wheat cropping system during rabi 2009 and 2010. Results showed that water soluble sources of phosphatic fertilizers (Single super phosphate, Diammonium phosphate, Urea ammonium phosphate) were found superior over partially water soluble (nitrophosphate) and mineral acid soluble (RP) sources in terms of grain yield and P uptake. With increasing levels of P from 60 to 120 kg P 2 O 5 ha-1 , grain yield and P uptake increased significantly. Cumulative mode of P application was found the best for grain yield and P uptake as compared to direct and residual mode. The available P, saloid-P and Al-P were positively and significantly correlated with grain yield (r = 0.829** to 0.894**), straw yield (r = 0.833** to 0.890**), P concentration in grain (r = 0.666* to 0.749*), and total P uptake (r = 0.860** to 0.928**). Multiple regression equations between yield and P uptake and various inorganic P fraction of soil also indicated that saloid-P and Al-P were the important forms of inorganic P and contributed mainly towards grain and straw yield and total P uptake.

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We show, both analytically and numerically, that for a nonlinear system making a transition from one equilibrium state to another under the action of an external time dependent force, the work probability distribution is in general asymmetric. PACS numbers:We consider a system in contact with a heat bath, which is driven out of equilibrium by an external time dependent force. This force drives it from an equilibrium state A to another equilibrium state B. It was shown by Jarzynski [1, 2, 3] that the equilibrium free energy difference, ∆F between these states can be related to the probability distribution of the work done W in taking the system from A to B. In particular, e −∆F KT = e −W KT *