There are some concepts that are accepted in our daily life but are not trivial in physics. One of them is the cluster property that means there exist no relations between two events which are sufficiently separated. ...There are some concepts that are accepted in our daily life but are not trivial in physics. One of them is the cluster property that means there exist no relations between two events which are sufficiently separated. In the works recently published by the author, the extensive and quantitative examination has been made about the violation of cluster property in the correlation function of the spin operator for the quantum spin system. These works have shown that, when we include the symmetry breaking interaction, the effect by the violation is proportional to the inverse of the system size. Therefore this effect is tinny since the system size is quite large. In order to find the effect due to the violation even when the size is large, we propose a new system where additional spins couple with the spin system on the square lattice, where the coupling constant between these systems being assumed to be small. Applying the perturbation theory, we obtain the effective Hamiltonian for the additional system. This Hamiltonian includes Curie-Weiss model that is induced by the violation of the cluster property. Then we find that this effective Hamiltonian has the factor which is the inverse of the system size. Since Curie-Weiss model, which is known to be exactly soluble, has to contain this factor so that the thermodynamical properties are well-defined, the essential factor for the Hamiltonian is determined by the coupling and the strength of the symmetry breaking interaction. Our conclusion is, therefore, that it is possible to observe the effect by the violation of the cluster property at the inverse temperature whose order is given by these parameters.展开更多
With the prevalent conception of self-replication (SR, a hallmark of living systems) as a non-equilibrium process subject to thermodynamic laws, a complementary approach derives the low energy quantum states arising f...With the prevalent conception of self-replication (SR, a hallmark of living systems) as a non-equilibrium process subject to thermodynamic laws, a complementary approach derives the low energy quantum states arising from a Hamiltonian that appears to be specific for bio-systems by its containing some strongly binding terms. The bindings attract <em>properties</em> of the template (T) and the reactants to form a replicate (R). The criterion for SR that emerges from the theory is that second order (bi-linear) interaction terms between degrees of motion of T-R and the thermal bath dominate negatively over a linear self-energy term, and thereby provide a binding between the attributes of T and R. The formalism (reminiscent of the Kramers-Anderson mechanism for superexchange) is from first principles, but hinges on a drastic simplification by modelling the T, R and bath variables on interacting qubits and by congesting the attraction into a single (control) parameter. The development relies on further simplifying features, such as Random Phase Approximations and an Effective Hamiltonian formalism. The entropic balance to replication is considered and found to reside in the far surroundings.展开更多
文摘There are some concepts that are accepted in our daily life but are not trivial in physics. One of them is the cluster property that means there exist no relations between two events which are sufficiently separated. In the works recently published by the author, the extensive and quantitative examination has been made about the violation of cluster property in the correlation function of the spin operator for the quantum spin system. These works have shown that, when we include the symmetry breaking interaction, the effect by the violation is proportional to the inverse of the system size. Therefore this effect is tinny since the system size is quite large. In order to find the effect due to the violation even when the size is large, we propose a new system where additional spins couple with the spin system on the square lattice, where the coupling constant between these systems being assumed to be small. Applying the perturbation theory, we obtain the effective Hamiltonian for the additional system. This Hamiltonian includes Curie-Weiss model that is induced by the violation of the cluster property. Then we find that this effective Hamiltonian has the factor which is the inverse of the system size. Since Curie-Weiss model, which is known to be exactly soluble, has to contain this factor so that the thermodynamical properties are well-defined, the essential factor for the Hamiltonian is determined by the coupling and the strength of the symmetry breaking interaction. Our conclusion is, therefore, that it is possible to observe the effect by the violation of the cluster property at the inverse temperature whose order is given by these parameters.
文摘With the prevalent conception of self-replication (SR, a hallmark of living systems) as a non-equilibrium process subject to thermodynamic laws, a complementary approach derives the low energy quantum states arising from a Hamiltonian that appears to be specific for bio-systems by its containing some strongly binding terms. The bindings attract <em>properties</em> of the template (T) and the reactants to form a replicate (R). The criterion for SR that emerges from the theory is that second order (bi-linear) interaction terms between degrees of motion of T-R and the thermal bath dominate negatively over a linear self-energy term, and thereby provide a binding between the attributes of T and R. The formalism (reminiscent of the Kramers-Anderson mechanism for superexchange) is from first principles, but hinges on a drastic simplification by modelling the T, R and bath variables on interacting qubits and by congesting the attraction into a single (control) parameter. The development relies on further simplifying features, such as Random Phase Approximations and an Effective Hamiltonian formalism. The entropic balance to replication is considered and found to reside in the far surroundings.
