Abstract
Macroscopic many-body systems always exhibit irreversible behaviors. However, in principle, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville equation, guarantees that the entropy of an isolated system does not change with time, which is quite confusing compared with the macroscopic irreversibility. We notice that indeed the macroscopic entropy increase in standard thermodynamics is associated with the correlation production inside the full ensemble state of the whole system. In open systems, the irreversible entropy production of the open system can be proved to be equivalent with the correlation production between the open system and its environment. During the free diffusion of an isolated ideal gas, the correlation between the spatial and momentum distributions is increasing monotonically, and it could well reproduce the entropy increase result in standard thermodynamics. In the presence of particle collisions, the single-particle distribution always approaches the Maxwell-Boltzmann distribution as its steady state, and its entropy increase indeed indicates the correlation production between the particles. In all these examples, the total entropy of the whole isolated system keeps constant, while the correlation production reproduces the irreversible entropy increase in the standard macroscopic thermodynamics. In this sense, the macroscopic irreversibility and the microscopic reversibility no longer contradict with each other.
Highlights
Considering an isolated ideal gas with N particles initially occupying only part of a box, after long enough time diffusion, the gas spreads all over the volume uniformly (Figure 1)
Notice that isolated quantum systems always follow the unitary evolution, and the system density matrix ρ(t) is described by the von Neumann equation ∂t ρ = i [ρ, Ĥ], which guarantees the von Neumann entropy SV [ρ] = −tr[ρln ρ] does not change with time. This result should apply for many-body systems, it seems inconsistent with the above entropy increase in the standard macroscopic thermodynamics
We study the correlation production in open and isolated thermodynamic systems
Summary
Considering an isolated ideal gas with N particles initially occupying only part of a box, after long enough time diffusion, the gas spreads all over the volume uniformly (Figure 1). Due to the practical restrictions of measurements, some correlation information hiding in the global state is difficult to be sensed, and that results to the appearance of the macroscopic irreversibility as well as the entropy increase In principle, such correlation understanding could apply for isolated systems. The reversibility of microscopic dynamics (for the global state) and the macroscopic irreversibility (for the partial information) coincide with each other This correlation understanding applies for both quantum and classical systems, and for both open and isolated systems; besides, it does not depends on whether there exist complicated particle interactions, and can be used to describe time-dependent non-equilibrium systems
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