Abstract
In this review paper we aim at illustrating recent achievements in anomalous heat diffusion, while highlighting open problems and research perspectives. We briefly recall the main features of the phenomenon for low-dimensional classical anharmonic chains and outline some recent developments on perturbed integrable systems, and on the effect of long-range forces and magnetic fields. Some selected applications to heat transfer in material science at the nanoscale are described. In the second part, we discuss of the role of anomalous conduction on coupled transport and describe how systems with anomalous (thermal) diffusion allow a much better power-efficiency trade-off for the conversion of thermal to particle current.
Highlights
Anomalous diffusion is a well-established concept in statistical physics and has been used to describe many diverse kinetic phenomena
How do the features of anomalous diffusion emerge when dealing with a many-body problem? What are the conditions for a statistical system composed of many interacting particles to yield effectively anomalous diffusion of particles or quasi-particles? Another question concerns how such anomalies in diffusion are related to transport and whether they can somehow be exploited to achieve some design principle, such as efficiency of energy conversion
It is important to consider the power-efficiency trade-off. This is a key problem in the field of finite-time thermodynamics [87], in relation to the fundamental thermodynamic bounds on the performance of heat engines, as well as the practical purpose of designing engines that, for a given output power, work at the maximum possible efficiency
Summary
Anomalous diffusion is a well-established concept in statistical physics and has been used to describe many diverse kinetic phenomena. The renewed research activity is motivated by the possibility of applying the thermodynamics and statistical mechanics to nano- and micro-sized systems, with applications in molecular biology, micro-mechanics, nano-phononics, etc. This involves dealing with systems far from the thermodynamic limit, where fluctuations and interactions with the environment are critically relevant and need to be understood in detail. Anomalous Heat Transport in Many-Body Systems we will mostly discuss one-dimensional chains) This amounts to saying that the anomalous dynamics of energy carriers is an emergent feature stemming from correlations of the full many-body dynamics. We conclude our review of the multifaceted problem of heat transport in classical systems with a short summary of possible extensions to the quantum domain, with reference to related open problems that merit attention in the near future
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