TITLE2: Quantum Finite Non-equilibrium Thermodynamics

Abstract: The laws of thermodynamics need to be generalized to the finite, quantum, non-equilibrium domain. It is by no means clear how to achieve this. In particular, how exactly are we to phrase the concepts of heat, work and entropy in the most general context? I plan to review some of the most relevant approaches and then, based on this, argue that: a) the usual entropies (due to Shannon and von Neumann, classically and quantumly respectively) are not sufficient to discuss state transformations (we need a more general concept of “majorisation”); b) the relationship between information and work requires us to use more generalized (Renyi) entropies; c) work is, in the quantum setting, not represented by an operator; d) any conclusions are highly sensitive to how we define the “rules of the game”; e) how do we include finite time transformations? These are just some of the issues we need to face, but there may be others en route to formulating the most general theory of thermodynamics. This is, of course, not only of pure academic interest, but is becoming of practical importance though our advances in nano and quantum technologies. If time permits, I will draw parallels between how we understand entanglement through local operation and how we formulate thermodynamical entropy.

Dr. Andrew Garner

TITLE1: Quantum Statistical Complexity

Abstract: The most interesting phenomena lie on the boundary between order and chaos. Unlike perfectly ordered or highly disordered systems, such as pendulums swinging according to Newtonian mechanics or ideal gases, the behaviour of complex systems cannot be characterised by a small number of variables. This includes phenomena stretching from self-organization and evolution, to neural networks and life itself. To fully understand these phenomena, we must be able to identify if a process is complex. One such method, the statistical complexity has a clear operational meaning: the higher a process’s statistical complexity, the more we must remember to simulate its behaviour.

In my lecture, I will discuss recent studies that consider the quantum analogue of this: the quantum statistical complexity. It will transpire that with access to quantum information processing, not only are some things less complex than they would appear classically, but for some systems, qualitative differences in the complexity’s behaviour may be observed. Thus, our notions of what is complex can diverge fundamentally when reality is viewed through the lens of quantum mechanics.

TITLE2: The Thermodynamics of Pattern Manipulation (Is simpler better?)

Abstract: Living organisms capitalize on their ability to predict their environment to maximize their available free energy, and invest this energy in turn to create new complex structures; a lion metabolizes the structure of an antelope (destroying it in the process), and uses the energy released to build more lion. Such processes constitute a manipulation of patterns – ordered sequences of data. Is there a preferred method by which this manipulation should be done? Occam’s razor (paraphrased: ``Everything should be made as simple as possible but no simpler,'') suggests that the best approach must avoid unnecessary complications. However, this is a guiding philosophical principle, rather than a physical law.

“Is simpler better?” can be quantified in science, provided that one explains what is meant both by “simpler” and by “better”. In my lecture, I shall do just this. I will present a framework for discussing the manipulation of patterns. Here, “simpler” will be related to the complexity of the pattern and the memory of the machine manipulating it; and “better” to the choice of machine that minimizes thermal dissipation. For machines that create patterns, I will show that the simpler approach is indeed the better one. However, contrary to intuition, when it comes to destroying a pattern to extracting work, we shall see that any device capable of making statistically accurate predictions can recover the entire free energy.