Jarzyski’s Equality and Crooks’ Fluctuation Theorem for General Markov Chains with Application to Decision-Making Systems

We define common thermodynamic concepts purely within the framework of general Markov chains and derive Jarzynski’s equality and Crooks’ fluctuation theorem in this setup. In particular, we regard the discrete-time case, which leads to an asymmetry in the definition of work that appears in the usual formulation of Crooks’ fluctuation theorem. We show how this asymmetry can be avoided with an additional condition regarding the energy protocol. The general formulation in terms of Markov chains allows transferring the results to other application areas outside of physics. Here, we discuss how this framework can be applied in the context of decision-making. This involves the definition of the relevant quantities, the assumptions that need to be made for the different fluctuation theorems to hold, as well as the consideration of discrete trajectories instead of the continuous trajectories, which are relevant in physics.     

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Ohne Zusammenfassung     

Experimental and theoretical investigations of the reactions NH(X 3Sigma-) + D(2S)-->ND(X 3Sigma-) + H(2S) and NH(X 3Sigma-) + D(2S)-->N(4S) + HD(X 1Sigmag+)

The rate coefficient of the reaction NH(X (3)Sigma(-))+D((2)S)-->(k(1) )products (1) is determined in a quasistatic laser-flash photolysis, laser-induced fluorescence system at low pressures. The NH(X) radicals are produced by quenching of NH(a (1)Delta) (obtained in the photolysis of HN(3)) with Xe and the D atoms are generated in a D(2)/He microwave discharge. The NH(X) concentration profile is measured in the presence of a large excess of D atoms. The room-temperature rate coefficient is determined to be k(1)=(3.9+/-1.5) x 10(13) cm(3) mol(-1) s(-1). The rate coefficient k(1) is the sum of the two rate coefficients, k(1a) and k(1b), which correspond to the reactions NH(X (3)Sigma(-))+D((2)S)-->(k(1a) )ND(X (3)Sigma(-))+H((2)S) (1a) and NH(X (3)Sigma(-))+D((2)S)-->(k(1b) )N((4)S)+HD(X (1)Sigma(g) (+)) (1b), respectively. The first reaction proceeds via the (2)A(") ground state of NH(2) whereas the second one proceeds in the (4)A(") state. A global potential energy surface is constructed for the (2)A(") state using the internally contracted multireference configuration interaction method and the augmented correlation consistent polarized valence quadrupte zeta atomic basis. This potential energy surface is used in classical trajectory calculations to determine k(1a). Similar trajectory calculations are performed for reaction (1b) employing a previously calculated potential for the (4)A(") state. The calculated room-temperature rate coefficient is k(1)=4.1 x 10(13) cm(3) mol(-1) s(-1) with k(1a)=4.0 x 10(13) cm(3) mol(-1) s(-1) and k(1b)=9.1 x 10(11) cm(3) mol(-1) s(-1). The theoretically determined k(1) shows a very weak positive temperature dependence in the range 250< or =TK< or =1000. Despite the deep potential well, the exchange reaction on the (2)A(") ground-state potential energy surface is not statistical.     

Effects of the cinnamoyl group on liquid crystal aligning capabilities on PCEMA surfaces

Four kinds of poly(4-methacryloyloxychalcone) (PCEMA) photo-alignment materials were synthesized. The effect of the cinnamoyl group on liquid crystal (LC) aligning capabilities and electro-optical characteristics of photo-aligned twisted nematic (TN) liquid crystal displays (LCDs) was investigated by photo-dimerization. Uniform NLC alignment by linearly polarized UV exposure at normal incidence on the PCEMA surfaces having a high density of cinnamoyl groups was observed. Also, excellent voltage-transmittance (V-T) curves for the photo-aligned TN-LCDs on the PCEMA surfaces was achieved. We find that the V-T and response time characteristics can be improved by increasing the density of cinnamoyl groups.     

Tunable cross-linked copolymer networks for improvement of physical performance

The ability to tune the physical properties of polymeric materials through the different compositions in copolymer networks is suitable for the strategy of materials accompanied by combined high mechanical strength and stretchability simultaneously. Here, we developed a practical and straightforward strategy of a copolymer network structure via controlling the compositions of the acrylic-based urethane copolymers of diurethane acrylate (DUA) and diurethane cyclic acrylate (DUCA) with hydrogen-bonds through photo-polymerization. The copolymer networks led to the development of a physically cross-linked structure between the amide groups of DUA and/or DUCA and the hydroxyl groups of pentaerythritol ethoxylate (PEEL) by hydrogen-bonds. Based on the rheological analysis, the composition of the copolymer networks had a significant effect on the control of physical properties and development of cross-linked structure and thus led to the tunable comprehensive properties including high elastic modulus, high chain mobility and high recovery performance with a higher proportion of DUCA in the copolymer networks. Consequently, the tunable copolymer networks based on the developed physically cross-linked structure can improve the elastic properties, recovery performance, and healing ability simultaneously, providing significant progress in the fields of coating and adhesive.