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Register a new userEntropy Production in Systems with Spontaneously Broken Time-Reversal
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We study the entropy production in non-equilibrium quantum systems without dissipation, which is generated exclusively by the spontaneous breaking of time-reversal invariance. Systems which preserve the total energy and particle number and are in contact with two heat reservoirs are analysed. Focussing on point-like interactions, we derive the probability distribution induced by the entropy production operator. We show that all its moments are positive in the zero frequency limit. The analysis covers both Fermi and Bose statistics.
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Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete exposition, the distribution of entropy production can be obtained analytically, but in general it is much harder. A recent development in solving the Fokker-Planck equation, in which the solution is written as a product of positive functions, enables the distribution to be obtained approximately, with the assistance of simple numerical techniques. Using examples in one and higher dimension, we demonstrate how such a framework is very convenient for the computation of stochastic entropy production in diffusion processes.
For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys Theta^2=-1, but no such a degeneracy exists when Theta^2=+1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when Theta^2=+1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.
We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.
We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov-Sinai entropy using a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov-Sinai entropy seen as functions of f admit a unique maximum denoted fmaxEP and fmaxKS. The behavior of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this article is that fmaxEP and fmaxKS have the same Taylor expansion at _rst order in the deviation of equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP (N) tends towards a non-zero value, while fmaxKS (N) tends to 0 when N goes to infinity. For values of N typical of that adopted by Paltridge and climatologists we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N_ such that fmaxEP and fmaxKS coincide, at least up to a second order parameter proportional to the non-equilibrium uxes imposed to the boundaries.
The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenbergs work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.
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