Saryal Sushant, Sadekar Onkar, Agarwalla Bijay Kumar
Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India.
Phys Rev E. 2021 Feb;103(2-1):022141. doi: 10.1103/PhysRevE.103.022141.
We investigate a transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production. We explore this relation in the context of energy transport in a bipartite setting for three exactly solvable toy model systems (two coupled harmonic oscillators, two coupled qubits, and a hybrid coupled oscillator-qubit system) and analyze the role played by the underlying statistics of the transport carriers in the TUR. Interestingly, for all these models, depending on the statistics, the TUR ratio can be expressed as a sum or a difference of a universal term which is always greater than or equal to 2 and a corresponding entropy production term. We find that the generalized version of the TUR, originating from the universal fluctuation symmetry, is always satisfied. However, interestingly, the specialized TUR, a tighter bound, is always satisfied for the coupled harmonic oscillator system obeying Bose-Einstein statistics. Whereas, for both the coupled qubit, obeying Fermi-like statistics, and the hybrid qubit-oscillator system with mixed Fermi-Bose statistics, violation of the tighter bound is observed in certain parameter regimes. We have provided conditions for such violations. We also provide a rigorous proof following the nonequilibrium Green's function approach that the tighter bound is always satisfied in the weak-coupling regime for generic bipartite systems.
我们研究了最近发现的热力学不确定性关系（TUR）的一个瞬态版本，该关系根据净熵产生为某些非平衡热力学可观测量提供了一种精度 - 成本权衡关系。我们在二分设置下的能量传输背景中，针对三个精确可解的玩具模型系统（两个耦合的谐振子、两个耦合的量子比特以及一个混合耦合的振子 - 量子比特系统）探索了这种关系，并分析了传输载流子的基础统计在TUR中所起的作用。有趣的是，对于所有这些模型，根据统计情况，TUR比率可以表示为一个总是大于或等于2的通用项与一个相应的熵产生项的和或差。我们发现，源自通用涨落对称性的TUR广义版本总是成立的。然而，有趣的是，对于服从玻色 - 爱因斯坦统计的耦合谐振子系统，更严格的TUR界限总是成立的。而对于服从费米样统计的耦合量子比特以及具有混合费米 - 玻色统计的混合量子比特 - 振子系统，在某些参数区域中观察到了对更严格界限的违反。我们给出了这种违反的条件。我们还采用非平衡格林函数方法提供了一个严格证明，即对于一般的二分系统，在弱耦合区域中更严格的界限总是成立的。
