Related papers: Thermodynamic-Complexity Duality: Embedding Comput…
Computational complexity is a particularly important objective. The idea of Landauer principle was extended through mapping three classic problems (sorting,ordered searching and max of N unordered numbers) into Maxwell demon thought…
One of the primary motivations of the research in the field of computation is to optimize the cost of computation. The major ingredient that a computer needs is the energy to run a process, i.e., the thermodynamic cost. The analysis of the…
The singularities prevalent in classical thermodynamics largely stem from the "postulate of equal a priori probabilities" neglecting the physical constraints imposed by computational complexity. This paper introduces Complexity Window…
We review and investigate the general theory of thermodynamics of computation, and derive the fundamental inequalities that set the lower bounds of the work requirement and the heat emission during a computation. These inequalities…
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information…
Turing Machines (TMs) are the canonical model of computation in computer science and physics. We combine techniques from algorithmic information theory and stochastic thermodynamics to analyze the thermodynamic costs of TMs. We consider two…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the…
The relationship between the thermodynamic and computational characteristics of dynamical physical systems has been a major theoretical interest since at least the 19th century, and has been of increasing practical importance as the…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate physical bounds on heat generation. A lower…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
We propose a new approach for multiverse analysis based on computational complexity, which leads to a new family of "computational" measure factors. By defining a cosmology as a space-time containing a vacuum with specified properties (for…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a…
One of the most intriguing features of string thermodynamics is thermal duality, which relates the physics at temperature T to the physics at inverse temperature 1/T. Unfortunately, the traditional definitions of thermodynamic quantities…
As a new step towards defining complexity for quantum field theories, we map Nielsen operator complexity for $SU(N)$ gates to two-dimensional hydrodynamics. We develop a tractable large $N$ limit that leads to regular geometries on the…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
Landauer's principle bounds the heat generated by logical operations, but in practice the thermodynamic cost of computation is dominated by the control systems that implement logic. CMOS gates dissipate energy far above the Landauer bound,…