We investigate a reversible polymerization process in which individual polymers aggregate and fragment at a rate proportional to their molecular weight. We find a nonequilibrium phase transition despite the fact that the dynamics are perfectly reversible. When the strength of the fragmentation process exceeds a critical threshold, the system reaches a thermodynamic steady state where the total number of polymers is proportional to the system size. The polymer length distribution has a sharp exponential tail in this case. When the strength of the fragmentation process falls below the critical threshold, the steady state becomes non-thermodynamic as the total number of polymers grows sub-linearly with the system size. Moreover, the length distribution has an algebraic tail and the characteristic exponent varies continuously with the fragmentation rate.
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal fundamental challenges that arise when attempting to implement arbitrary computations reversibly. Firstly, the requirements of thermodynamic reversibility inevitably lead to an intricate design. Secondly, thermodynamically reversible UTMs, unlike simpler devices, must also be logically reversible. Finally, implementing multiple distinct computations in parallel is …
In this article a definition of reversible processes in terms of differences in intensive Thermodynamics properties (Affinities) is proposed. This definition makes it possible to both define reversible processes before introducing the concept of entropy and avoid the circularity problem that follows from the Clausius definition of entropy changes. The convenience of this new definition compared to those commonly found in textbooks is demonstrated with examples.
We analyze the time-reversible mechanics of two irreversible simulation types. The first is a dissipative one-dimensional heat-conducting oscillator exposed to a temperature gradient in a three-dimensional phase space with coordinate $q$, momentum $p$, and thermostat control variable $ζ$. The second type simulates a conservative two-dimensional $N$-body fluid with $4N$ phase variables $\{q,p\}$ undergoing shock compression. Despite the time-reversibility of each of the three oscillator equations and all of the $4N$ manybody motion equations both types of simulation are irreversible, obeying th…
Onsager's phenomenological equations successfully describe irreversible thermodynamic processes. They assume a symmetric coupling matrix between thermodynamic fluxes and forces. It is easily shown that the antisymmetric part of a coupling matrix does not contribute to dissipation. Therefore, entropy production is exclusively governed by the symmetric matrix even in the presence of antisymmetric terms. In this work we focus on the antisymmetric contributions which describe isentropic oscillations and well-defined equations of motion. The formalism contains variables that are equivalent to momen…
The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for and analysis of classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorin…
Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions with intended application of being used as a quick way of generating numerous other inequalities such as the Weighted Means Inequality. The proofs also serve as a way of establishing the equivalence of the Planck's statement of the Second Law and the positivity of specific heats.
According to a well-known principle of thermodynamics, the transfer of heat between two bodies is reversible when their temperatures are infinitesimally close. As we demonstrate, a little-known alternative exists: two bodies with temperatures different by an arbitrary amount can completely exchange their temperatures in a reversible way if split into infinitesimal parts that are brought into thermal contact sequentially.
We investigate the performance of majority-logic decoding in both reversible and finite-time information erasure processes performed on macroscopic bits that contain $N$ microscopic binary units. While we show that for reversible erasure protocols single-unit transformations are more efficient than majority-logic decoding, the latter is found to offer several benefits for finite-time erasure processes: Both the minimal erasure duration for a given erasure and the minimal erasure error for a given erasure duration are reduced, if compared to a single unit. Remarkably, the majority-logic decodin…
Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex …
According to Landauer's principle, erasure of information is the only part of a computation process that unavoidably involves energy dissipation. If done reversibly, such an erasure generates the minimal heat of $k_BT\ln 2$ per erased bit of information. The goal of this work is to discuss the actual reversal of the optimal erasure which can serve as the basis for the Maxwell's demon operating with ultimate thermodynamic efficiency as dictated by the second law of thermodynamics. The demon extracts $k_BT\ln 2$ of heat from an equilibrium reservoir at temperature $T$ per one bit of information …
Thermodynamic process at zero-entropy-production (EP) rate has been regarded as a reversible process. A process achieving the Carnot efficiency is also considered as a reversible process. Therefore, the condition, `Carnot efficiency at zero-EP rate' could be regarded as a strong equivalent condition for a reversible process. Here, however, we show that the detailed balance can be broken for a zero-EP rate process and even for a process achieving the Carnot efficiency at zero-EP rate in an example of a quantum-dot model. This clearly demonstrates that `Carnot efficiency at zero-EP rate' or just…
This comment is written on the article by Hiroyasu Koizumi, in which an alternative theory of superconductivity is proposed. No Joule heating is predicted in this theory unlike the conventional BCS-London theory of superconductivity. The theory is based on the author's opinion that the kinetic energy for the supercurrent is converted into the energy of the magnetic field during the transition of a bulk superconductor into the normal state in the presence of a magnetic field. The Comment indicates that this opinion cannot be correct, since the kinetic energy is much less than the energy of the …
