Entropy gradient

From Eq 2.10 one can express the enthalpy and entropy gradients between two temperatures. 

An instability-induced grand transition from quantum vacuum to material existence might have created our universe. Energy and entropy gradients mediated duality developments and transitions between fermions and bosons, particles and waves, structure and phase into the process-information dualities of life patterns. At the interface to the universe, life patterns developed a preliminary finite duality between existent matter and self-consciousness fields. By this grand transition a facility of awareness beyond space and time originated that transformed its theses/antitheses tensions into creativity. 

Assume that terms associated with entropy gradients (coefficient D in the equation of motion) are negligible in comparison with those corresponding to density gradients. Then, a simplified... 

A high-shear gradient can lead to the deformation of macromolecular coils. The entropy gradient thus... 

Diffusion may be defined as the movement of a species due to a concentration gradient, which seeks to maximize entropy by overcoming inhomogeneities within a system. The rate of diffusion of a species, the flux, at a given point in solution is dependent upon the concentration gradient at that particular point and was first described by Pick in 1855, who considered the simple case of linear difflision to a planar surface ... 

We mentioned above that a typical problem for a Boltzman Machine is to obtain a set of weights such that the states of the visible neurons take on some desired probability distribution. For example, the task may he to teach the net to learn that the first component of an Ai-component input vector has value +1 40% of the time. To accompli.sh this, a Boltzman Machine uses the familiar gradient-descent technique, but not on the energy of the net instead, it maximizes the relative entropy of the system. 

Eckart, criteria, 264, 298 procedure, 267 Effective charge, 274, 276 Effective Hamiltonian, 226 Elastic model, excess entropy calculation from, 141 of a solid solution, 140 Electric correlation, 248 Electric field gradient, 188, 189 Electron (s), 200... 

Let [1], [2], [8] be any three modifications of a substance which can exist together in equilibrium at a triple point, and let t i, r2, r3 be their specific volumes su s2, s3, their entropies per unit mass. The gradients of the p-T curves at the triple point are given by the latent-heat equations ... 

Electric field gradient tensor 24 Entanglements 124 Entropy model 200,201 Epoxy composites 192... 

Temperature-entropy diagram, water and steam 814 Temperature gradient, flow over plane surface 688... 

The first role of a reservoir is to impose on the system a gradient that makes the subsystem structure nonzero. The adiabatic flux that consequently develops continually decreases this structure, but the second role of the reservoir is to cancel this decrement by exchange of variables conjugate to the gradient. This does not affect the adiabatic dynamics. Hence provided that the flux is maximal in the above sense, then this procedure ensures that both the structure and the dynamics of the subsystem are steady and unchanging in time. (See also the discussion of Fig. 9.) A corollary of this is that the first entropy of the reservoirs increases at the greatest possible rate for any unconstrained flux. 

The end effects have been neglected here, including in the expression for change in reservoir entropy, Eq. (178). This result says in essence that the probability of a positive increase in entropy is exponentially greater than the probability of a decrease in entropy during heat flow. In essence this is the thermodynamic gradient version of the fluctuation theorem that was first derived by Bochkov and Kuzovlev [60] and subsequently by Evans et al. [56, 57]. It should be stressed that these versions relied on an adiabatic trajectory, macrovariables, and mechanical work. The present derivation explicitly accounts for interactions with the reservoir during the thermodynamic (here) or mechanical (later) work,... 

The present analysis shows that when a thermodynamic gradient is first applied to a system, there is a transient regime in which dynamic order is induced and in which the dynamic order increases over time. The driving force for this is the dissipation of first entropy (i.e., reduction in the gradient), and what opposes it is the cost of the dynamic order. The second entropy provides a quantitative expression for these processes. In the nonlinear regime, the fluxes couple to the static structure, and structural order can be induced as well. The nature of this combined order is to dissipate first entropy, and in the transient regime the rate of dissipation increases with the evolution of the system over time. 

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