Related papers: Thermodynamic-Complexity Duality: Embedding Comput…
It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT(ln d -S) amount of work. However, the usual arguments based on Szilard engine are not fully rigorous. Here we prove…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
Digital computers implement computations using circuits, as do many naturally occurring systems (e.g., gene regulatory networks). The topology of any such circuit restricts which variables may be physically coupled during the operation of a…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and…
In this paper, we study the physical significance of the thermodynamic volumes of AdS black holes using the Noether charge formalism of Iyer and Wald. After applying this formalism to study the extended thermodynamics of a few examples, we…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008] and [K. Tadaki, Proceedings of…
If the 20th century was known for the computational revolution, what will the 21st be known for? Perhaps the recent strides in the nascent fields of molecular programming and biological computation will help bring about the 'Coming Era of…
We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete…
There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit…
A measure of how sensitive the entanglement entropy is in a quantum system, has been proposed and its information geometric origin is discussed. It has been demonstrated for two exactly solvable spin systems, that thermodynamic criticality…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, which states that…
Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum…
It is assumed that the holographic complexities such as the complexity-action (CA) and the complexity-volume (CV) conjecture are dual to complexity in field theory. However, because the definition of the complexity in field theory is still…